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FROM Magoosh Blog: GMAT Reading Comprehension: Strategies for the 6 Question Types and Example Passage


Virtually all GMAT Reading Comprehension questions fall into these 6 categories: main idea, detail, inference, out of context, logical structure, and author’s tone. Familiarizing yourself with each type of reading comprehension prompt will allow you to think more like the test-writers and root out common traps.

GMAT Reading Comprehension Question Type 1: Find the Main Idea
Of all the reading comprehension (RC) types, “main idea” questions are the most common. You can expect the GMAT to ask this question often. Identifying the main idea is a quintessential skill. Practice identifying it with each passage you tackle. It will help to read at a relaxed pace (2.5 minutes for a short RC passage, 3.5 for a long passage). It will help to practice taking notes. It will also help to practice repeatedly from reputable sources, like the Offical Guide.

As you study, always check the official answers and read the explanations, regardless of whether you got the question right or wrong. Doing so will allow you to think more like the test-writers. By practicing diligently, you’ll begin to notice how to weed out trap answers and how to select the best answer from the available options.

GMAT Reading Comprehension Question Type 2: Detail
Detail questions tend to be one of the most straight forward question types because they literally ask you about something that you can lookup in the passage. Detail Questions are readily identifiable if you know what to look for. “According to the passage,” is the biggest clue that you’re facing a Detail Question.

GMAT Reading Comprehension Question Type 3: Inference
Good authors are not explicit about everything. While they say some things directly, they imply others. Inference questions test your ability to read between the lines and figure out what the author is indirectly implying.

On the GMAT, be careful to stay hyper-faithful to the passage. A correct implication is something that was not explicitly stated but must be true. In other words, an inference must be a direct logical consequence of what was written. For example, if the passage reads, “Ben has been to every country in Europe at least once”, we cannot necessarily infer that “Ben enjoys traveling” — maybe Ben hates traveling, but he is required to travel for work! By contrast, an undeniable implication is: “Ben has been to Portugal at least once.” That’s the level of logical undeniability that you should seek in inference question answer choices.

GMAT Reading Comprehension Question Type 4: Out of Context
There are two subcategories for this reading comprehension type. Some of these questions will present a new concept—one not discussed at all in the text—and ask you what the author would think about it. Expect these to begin with something like: “How would the author of the passage most likely respond to the assertion that…?” In order to answer these questions, you need to deduce the perspective and preferences of the author from the passage

Alternatively, “out of context” questions may ask you to compare something in the passage to a hypothetical example from a completely different situation. “The compromised situation of the raccoon described in line X is most like …”, and then the correct answer could be something like “a ballerina with a broken foot.” For these questions, your mission is to focus on what is essential to the situation or relationship in its most rigid logical form.

In both cases, however seemingly remote the focus of the question is, the correct answer should still resonate with the author’s main idea as demonstrated by the passage.

GMAT Reading Comprehension Question Type 5: Logical Structure
Some questions will ask about the structure of the passage as a whole: Does the author present her own new idea? Does the author contrast two ideas, evenhandedly showing the strengths and weaknesses of both? Does the author sharply criticize a particular position or perspective? Sometimes this question is phrased as: “What would be the best title for this passage?”

Here, the main idea and paragraph summaries you formulate in your notes will be invaluable. Another huge help will be the “logical direction” words — “moreover”, “although”, “ironically”, “but”, etc. Always pay attention to these words as you read, notice the way they shape the paragraph, and you will start to develop an intuitive sense of the logical structure of the passages.

GMAT Reading Comprehension Question Type 6: Author’s Tone
This is tricky, because unlike the extreme opinions typical of the talking heads in today’s media, all the opinions and perspectives of GMAT authors will be moderated and nuanced. An author who judges something “promising” is wildly enthusiastic about it. An author who deems something “less than satisfactory” is completely slamming it. An author who finds something “troubling” is essentially take-all-his-toys-and-go-home upset about it.

If vivid emotions are bright colors, then GMAT passages don’t get any more colorful than pastels. Pay attention to adjectives and any words that an emotional charge: these are the ones that will allow you to figure out the author’s tone.

It’s exceedingly important to remember this about the GMAT: the tone of the passage will avoid extremes. Thus, the correct answers to tone questions will avoid extremes as well. If the correct answer to a tone question is “skeptical”, wrong answers could include “dismissive” or “vengeful”—words that simply are two extreme for the tenor of GMAT RC. As you read, pay special attention to word choice. Subtlety is key for mastering this reading comprehension question type.

Sample Reading Comprehension Passage
Most educated people of the eighteenth century, such as the Founding Fathers, subscribed to Natural Rights Theory, the idea that every human being has a considerable number of innate rights, simply by virtue of being a human person. When the US Constitution was sent to the states for ratification, many at that time felt that the federal government outlined by the Constitution would be too strong, and that rights of individual citizens against the government had to be clarified.  This led to the Bill of Rights, the first ten amendments, which were ratified at the same time as the Constitution.  The first eight of these amendments list specific rights of citizens.  Some leaders feared that listing some rights could be interpreted to mean that citizens didn’t have other, unlisted rights.  Toward this end, James Madison and others produced the Ninth Amendment, which states: the fact that certain rights are listed in the Constitution shall not be construed to imply that other rights of the people are denied

Constitutional traditionalists interpret the Ninth Amendment as a rule for reading the rest of the constitution.  They would argue that “Ninth Amendment rights” are a misconceived notion: the amendment does not, by itself, create federally enforceable rights.   In particular, this strict reasoning would be opposed to the creation of any new rights based on the amendment.  Rather, according to this view, the amendment merely protects those rights that citizens already have, whether they are explicitly listed in the Constitution or simply implicit in people’s lives and in American tradition.

More liberal interpreters of the US Constitution have a much more expansive view of the Ninth Amendment.  In their view, the Ninth Amendment guarantees to American citizens a vast universe of potential rights, some of which we have enjoyed for two centuries, and others that the Founding Fathers could not possibly have conceived.  These scholars point out that some rights, such as voting rights of women or minorities, were not necessarily viewed as rights by the majority of citizens in late eighteenth century America, but are taken as fundamental and unquestionable in modern America.  While those rights cited are protected specifically by other amendments and laws, the argument asserts that other unlisted right also could evolve from unthinkable to perfectly acceptable, and the Ninth Amendment would protect these as-yet-undefined rights.

 

Reading Comp. Practice Questions
1) The author cites the scholars referring to “voting rights of women or minorities” in order to

      (A) cite unquestionably justified Ninth Amendment rights
 

      (B) demonstrate how changing priorities can alter perspectives on fundamental human rights
 

      (C) argue for the modern extension of Natural Rights Theory
 

      (D) refute the traditionalist interpretation of the Ninth Amendment
 

           (E) champion the rights of all citizens in the democratic process
2) Constitutional scholars of both the traditionalist and liberal views would agree that “Ninth Amendment rights”

      (A) accommodate shifts in cultural values with respect to issues affecting human rights
 

      (B) cannot serve as the basis of legal decisions
 

      (C) are directly reflected in our understanding of who can and can’t vote
 

      (D) are not stated explicitly in the Bill of Rights
 

          (E) extend the idea of Natural Rights Theory
3) According to the passage, what would the Ninth Amendment imply about a right to “a trial by jury”, guaranteed in the Seventh Amendment of the US Constitution?

      (A) The Ninth Amendment would provide direct support for this right.
 

      (B) The Ninth Amendment would not support this right directly, but would support all the logistics that would allow citizens to exercise this right.
 

      (C) The Ninth Amendment would apply to trials that fall outside the jurisdiction of Federal Courts.
 

      (D) The Ninth Amendment would apply to all trials that do not involve Constitutional Law
 

          (E) The Ninth Amendment is irrelevant to any right mentioned explicitly in the Bill of Rights.
4) In the view of James Madison and the other Founding Fathers, the Ninth Amendment limits the power of the central Federal government by

      (A) preventing constitutionally listed rights from being viewed as exhaustive
 

      (B) giving the citizens rights in every area not explicitly addressed by the law
 

      (C) codifying a vast universe of federally enforceable rights
 

      (D) guaranteeing, in the text of US Constitution, all rights held by Natural Rights Theory
 

          (E) ensuring all citizens are able to vote and, thus, choose the democratic leaders
5) The primary purpose of the passage is to

      (A) clarify the most proper interpretation of an amendment
 

      (B) argue for a broader perspective on human rights and their legal protection
 

      (C) contrast historical perspectives of an amendment to its modern legal reading
 

      (D) explain the motivation for an amendment and the ambiguity this amendment presents
 

          (E) demonstrate how the Founding Fathers’ intentions have been distorted by subsequent legal proceedings.
 

Practice Question Solutions
1) This quote appears in the third paragraph, in which the author is discussing liberal interpretations of the Ninth Amendment.

(B) is the credited answer.  Scholars cited indicated these rights as examples of rights the Founding Fathers wouldn’t have recognized but which modern Americans take for granted.  In other words, the change in priorities over the past two hundred years has “alter[ed our] perspectives on fundamental human rights.”

Choice (A) is wrong, because as the passage points out, these particular rights are guaranteed in other parts of the Constitution, and anything stated explicitly in the Constitution is not relevant to the Ninth Amendment.

Choice (C) is wrong, because whether these rights would in any way be considered as part of Natural Rights Theory (a 17th & 18th century theory of white European males) is not discussed at all in the third paragraph.

Choice (D) is wrong, because while this quote does support the liberal interpretation of the Ninth Amendment, and therefore raises an objection to the traditional interpretation, to say that it “refutes” the latter is far too strong.   It merely raises an objection for which the traditionalist may well have a satisfactory answer.

Choice (E) is wrong, because it’s far too broad.  The author is specifically talking about readings of the Ninth amendment, so conclusions about “the rights of all citizens” is a much broader concern than is being addressed in this passage.

2) Notice that the two sides vehemently disagree about the whole notion of “Ninth Amendment rights” — the liberals might argue for them, but the traditionalists thing the term itself is a fallacy.  These two sides would only agree on something very basic.

(D) is the credited answer.  The amendment itself says that it addresses rights that are not stated explicitly in the Bill of Rights.  Both sides would have to agree — any right that is explicitly stated in the Bill of Rights is not a “Ninth Amendment right.”

Choice (A) is wrong, because this is something the liberals would embrace and the traditionalists would reject.

Choice (B) is wrong, because while we know the traditionalists accept this, it’s implied that the liberals reject it.

Choice (C) is wrong, because it focuses on a detail: the detail of voting rights isn’t even directly related to the Ninth Amendment.

Choice (E) is wrong, because it’s not completely clear where either side in the modern debate stands with respect to this much older theory.   Moreover, we suspect that, if they have opinions at all, the liberals would have a much broader understanding of how the Ninth Amendment extend the idea of Natural Rights Theory, while traditionalists argue that the Ninth Amendment does extend anything.

3) The right to “a trial by jury” is an explicitly listed right in the Bill of Rights.  As such, the Ninth Amendment does not apply to it at all.  The whole point of the Ninth Amendment is that it applies only to rights not explicitly addressed in the Constitution.  (E) is the credited answer.  All the other answers, about the Ninth Amendment supporting this right or applying in one way or another, are incorrect.

4) (A) is the credited answer.  The Bill of Rights listed certain rights, but Madison and others did not want this list read as if it were “exhaustive” — that is, as if it were a complete list to which nothing else could be added.  This is precisely the motivation for the Ninth Amendment, explained in the first paragraph.

Choice (B) is wrong, because nothing in the passage says that the amendment automatically gives people specific tangible rights.

Choice (C) is wrong, because while the liberals might argue that it supports several rights, these new rights are not “encoded”, that is guaranteed as law.

Choice (D) is wrong, because the passage doesn’t even discuss what rights are held my Natural Rights Theory: furthermore, presumably some of those rights, such as freedom of speech, were already guaranteed in other amendments of the Bill of Rights, so the Ninth Amendment wouldn’t apply to those.

Choice (E) is wrong, because it picks up on a detail of the passage, from modern times, and says it applies to Founding Fathers.   The fundamental voting rights that the Founding Fathers recognized were written explicitly in other parts of the Constitution, and are not in the “unwritten” area covered by the Ninth Amendment.

5) (D) is the credited answer.  The passage gives us some history, about why the Founding Fathers felt this amendment was needed, and then the last two paragraphs exploring different ways of interpreting this amendment: because the amendment lends itself to such radically different interpretations, we can say it contains “ambiguity.”

Choice (A) is wrong, because the passage does not draw any conclusions on whether the traditionalist or liberal interpretation is better.

Choice (B) is wrong, because this answer would imply that the purpose was to agree with the liberal interpretation, but the passage does not clearly valorize one view over the other.

Choice (C) is wrong, because the primary contrast is not between 18th century readings vs. modern readings, but between two modern readings.

Choice (E) is wrong, because we don’t actually know the Founding Fathers’ intentions — the passages says very little about this, and its’ rather unclear whether Founding Fathers as a group would have agreed more with the liberal or the traditionalist interpretation of the Ninth Amendment.

 

If you’re looking to strengthen your Reading Comprehension skills, Magoosh is here to help! Magoosh GMAT offers high-quality, affordable test prep to help you reach your score goals. Get access for a year with premium, or try us for free with a 1-week trial!

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FROM Magoosh Blog: Introduction to GMAT Critical Reasoning and Practice Questions


What is GMAT critical reasoning?

GMAT Critical Reasoning is one of the two question types found in the GMAT Verbal section. All CR questions contain a prompt (usually 100 words or fewer) that presents some sort of argument, which is followed by a question stem and 5 answer choices. The questions revolve around a logical analysis of the core argument and might involve strengthening it, weakening it, finding its underlying assumption, etc. GMAT Critical Reasoning tests your critical thinking and logic skills more than your reading skills.

Logical reasoning is also one of the most important skills in the business world. Whether to decide upon the best sales strategy, to understand what motivates your customers, or to navigate investor concerns, well presented, logical arguments are the bedrock of successful business management. An effective manager demonstrates skills in addressing the following: How would I strengthen or weaken this argument? What is the assumption of this argument? What further evidence would I need to evaluate this argument? In other words, a real-life manager needs to apply all the skills required for success on GMAT Critical Reasoning questions.

The 8 Critical Reasoning Question Types

The eight broad categories of GMAT Critical Reasoning questions are:

1) weaken the argument/find the flaw in the argument
2) strengthen the argument
3) find the assumption
4) draw inference/conclusion
5) structure of the argument, including boldface structure questions and dialogue structure questions
6) paradox
7) evaluate the conclusion
8 ) complete the argument

Types #1-4 account for most GMAT CR questions. You can find out more about each one of these types in the linked blog articles.

Top Tips for Improving in GMAT Critical Reasoning
Tip #1 – Read the Question First!
Read the question stem before reading the argument. This will help you know which type of question you are going to have to answer. Then, you can read the argument with that question in mind.

Tip # 2 – Know the Different Elements of an Argument

In reality, every argument has three key components:

  • A premise(s), which are the facts or reasons that form the foundation of the argument.
  • A conclusion, which is usually the message of the argument and is supported by the premise(s).
  • An assumption, which is usually not stated in the argument but must be true for the conclusion to be valid. In other words, if the assumption is found to be false, the entire argument will fall apart.

If you have a mathematical bent of mind, think of these components through the following equation:

Premise + (Unstated) Assumption + (extra context/background info) = Conclusion

The two that are usually easier to identify are the conclusion and the premise. But! It’s important to note that more complex CR question types might not even have a stated conclusion or easily identifiable premise. However, when those elements are present, it is important to think about the underlying assumption that is holding the argument together. Your job is never to question the facts of the argument. You have to take anything stated as truth. Your job is to find the unstated assumption and question the gap between the facts and the conclusion. Ask yourself: What did the author need to be true in order to reach the conclusion?

To become good at solving CR questions, it is important to become good at analyzing the argument and identifying all these components of the argument. You can find more details regarding assumption questions here.

Tip #3 – Know What You’re Looking For Beforehand

In all Critical Reasoning questions, the GMAT gives one correct answer and four tempting and potentially confusing statements for the other choices. Folks who read the argument & question and then wander aimlessly into the answer choices without any further thought are asking to be perplexed, and, chances are, they spend much longer than necessary on the questions.

Go into the question with an idea of what you seek. For types #1-3, the best thing to do is to find the assumption of the argument — reaffirming or undercutting the assumption of an argument is the most powerful way to strengthen or weaken it. Finding the assumption may also be helpful in finding the flaw of the argument (if the flaw is a faulty assumption).

For the other question types, you will be less able to predict what the answer will be; still, formulating the task in your own words will help you. In your own words, what is the structure of the argument? What is the paradox that needs to be resolved? What kind of information would be required to evaluate the conclusion? etc. The more clearly you understand what type of information or argument will satisfy the question, the more quickly you will find it.

Tip #4: Read EXACTLY what is written

The majority of mistakes in the critical reasoning section often boil down to the same fundamental error that students make: misreading the argument, question stem, or one of the choices. Furthermore, the argument is limited to the topic presented. Any answer choice that alters or moves away from the topic of the argument is a trap.

It is extremely important to take your time, stay engaged with the argument and read EXACTLY what is written without trying to paraphrase it. A single word can change the meaning of the conclusion or what piece of information can make that conclusion invalid. It might seem beneficial to simplify certain details or ignore certain modifiers that seem like ‘extra’ information for the argument, but that is what can get you into trouble. Reading carefully and noticing every modifier or any extra information in the passage is the best way to avoid mistakes.

Tip #5: Look for Four Wrong Answers, Not the Correct One.

Almost all Critical Reasoning questions will have at least a couple of choices that are clearly incorrect. When struggling through the confusing options, your focus should be to first find those low fruits and eliminate them. In the first pass, only eliminate the option choices that you are completely sure are incorrect. You can always go through the options again and iteratively make eliminations to find four incorrect choices. This will also allow you to “narrow the field” and focus on the more difficult or confusing choices that require slightly more focus and attention. Once you have done that, the last remaining choice, no matter how confusing or how strange, has to be the correct answer.

GMAT Critical Reading Practice Questions (with Explanations)
Click here for a video answer and explanation to the first of our GMAT Critical Reasoning Questions![/b][/list]

Click here for a text answer and explanation to GMAT Critical Reasoning Question 1
From all the evidence given, it seems that BCC (and the independent consultants) have taken all costs into account, and the analysis reveals that they will reap a considerable profit. In order to call this into question, we have to come up with some major unanticipated cost that would not be something already considered in this analysis.

(D) is the credited answer. First of all, laser printers and photocopiers are very common devices in office spaces, so we good reason to think that many of Megalimpet’s tenants will use these. If the toner degrades the carpet, that’s a huge additional expense for BCC, because their contract includes “ongoing maintenance” — i.e. replacing any carpet that needs replacing. Finally, nothing in the argument stem gives us any indication that this problem was on anybody’s radar, so this well could be an unexpected or unanticipated expense for BCC. Therefore, it most calls into question the idea that BCC will make a huge profit.

(A) & (C) are all expenses that would have been very clear to BCC and to its independent consultants, and therefore all of these would have had to have been taken into account when the financial analysis of the bid was made. There is no reason any of these expenses would be unanticipated.

(B) speaks to BCC previous experience, which, if anything, would tend to suggest they know what they are talking about. If anything, this would tend to strengthen the argument, not weaken it.

(E) only compares BCC to the second lowest bid, but we have no idea about that company, what it did or did not take into account in their bid, and what their overall costs might be. There are too many unknowns for this piece of information, by itself, to have any substantial impact on the argument.

Answer = D
Click here for a video answer and explanation to GMAT Critical Reasoning Question 2![/b][/list]

Click here for a text answer and explanation to GMAT Critical Reasoning Question 2
The statement by the front office of the baseball franchise seems, on the surface, not to take the basic facts into account. If we want to strengthen this position, there must be some alternate explanation for the drop in attendance.

Part of strengthening the franchise’s position would be weakening the original position: namely, that the team’s poor play explains the drop in attendance.

(C) is the credited answer. If other minor league teams also experience a drop this week, there must be something global in this market affecting all teams. We don’t know what this factor is, but it’s something that touches all teams, not just those that played bad last week. This provides a cogent alternative explanation, even though we don’t know the specific nature of the factor causing the drop in attendance.

Both (A) & (D) strengthen the original position, namely, that the team’s poor play explains the drop in attendance. In order to strengthen the baseball franchise’s position, we have to weaken this original position.

Choice (B) essentially accuses the baseball franchise of lying, or at least bluffing, which hardly strengthens their position.

Choice (E) simply adds to the paradox: if the closest MLB team is far away and folks typically don’t go there, then there would be more demand for the local minor league baseball. Given that demands, a drop in attendance doesn’t make as much sense. This choice adds to the confusing without explaining anything.

Answer = C
Click here for a video answer and explanation to GMAT Critical Reasoning Question 3![/b]

Click here for a text answer and explanation to GMAT Critical Reasoning Question 3
The evidence says: all the ETS hackers were FANTOD programmers. What the colleges seem to be assuming is the converse: all FANTOD programmers are hackers. Of course, there is no direct evidence for this converse. Presumably there are some students who learn FANTOD in good faith and who are not hackers, but because of the assumption the colleges are making, these students are faced with extra challenges, such as having their justly achieved SAT scores disregarded and being forced to take additional admission tests.

(C) is the credited answer. Since there is no evidence for the converse statement, we have reason to believe there are FANTOD programmers who are entirely innocent of any hacking, yet those very students will have their perfectly valid SAT scores dismissed and will have to take a new test to achieve admission: this certainly would not be fun, would not be fair, and could place them at a disadvantage with respect to all the non-programming students who could just take the ordinary SATs and be done with all testing.

(A) assumes too much based on the information provided in the prompt. Specifically, we only know about a specific group of those with FANTOD knowledge: those who used it to hack into ETS. Therefore, we cannot make any airtight conclusions about “most people”. It is very possible that most people who know FANTOD use it for purposes other than hacking.

(B) might be true, but it’s much too broad. This is about the much larger issue of what is the best way for colleges to determine who should be admitted. This entire argument is focused quite specifically on the FANTOD programmers and the issues associated with them.

We have absolutely no evidence for (D). All we know is that, whatever scores those hackers achieved on the real SAT, they falsified the records to make them higher. We don’t know if those scores were already high, and we certainly can draw no conclusion about all the students who know how to program in FANTOD who are not hackers. In fact, one might suspect the opposite, that folks bright enough to figure out this sophisticated programming language might be more intelligent and more successful on average, but even that we strictly can’t assume. Therefore, we can’t draw a clear conclusion about this.

(E) is a tricky one. We are told that some colleges took a certain set of special measures. We are given no information on what the other colleges did. Did they take another set of special measures? Did they not address the issue at all? We don’t know. Therefore, we can’t draw a clear conclusion along these lines.

Answer = C
Click here for a video answer and explanation to GMAT Critical Reasoning Question 4![/b]

Click here for a text answer and explanation to GMAT Critical Reasoning Question 4
The argument makes a number of factual statements. Art in the first half of the 20th century are, or could be considered, beautiful. Works by artists in the latter half of the 20th century are not supposed to be beautiful, and even, are supposed to be devoid of beauty. Then the argument draws a bold powerful conclusion: therefore, they are not art! The assumption seems to be something that links beauty to whether something qualifies as art. We definitely need an answer to speak to the question: what does, or doesn’t, qualify as art?

(C) is credited answer. If something needs to be beautiful, or potentially beautiful, to qualify as art, then this would explain that works that “no one could find beautiful” would fall outside the author’s definition of art.

The other answers are all quite tempting, because we could imagine an art professor or someone in an art class arguing for any one of them.

(A) is irrelevant. Critics & the general public might have different appraisals, but what one or the other thinks does not, in and of itself, seem to determine whether something is art.

(B) is also irrelevant: who determines the meaning is a separate question from whether the work qualifies at art in the first place. (BTW, exceedingly few modern critics would accept the interpretive idea contained in choice .)

(D) is undeniably true, but not relevant: again: it provides no standard by which we could say the former objects are art and the latter objects aren’t.

(E) is a far-flung idea, unrelated to the discussion. The passage doesn’t address the issue of whether any works of art are intellectually engaging.

Answer = C
Click here for a video answer and explanation to GMAT Critical Reasoning Question 5![/b]

Click here for a text answer and explanation to GMAT Critical Reasoning Question 5
Answer = C
prehistoric fire were found in Tanzania. The author says that Homo erectus made these fires, and that there’s no reason to assume Homo ergaster did. What is a necessary assumption?

The credited answer is choice (A). Homo erectus had to be as far south as Tanzania—if they were not, there would be no way they could have made those fires there, which would seem to indicate that Homo ergaster made them after all. Negating this statement devastates the argument, which is a confirmation that we have an assumption.

Whatever might have caused Homo erectus to master fire doesn’t clarify who made those fires in Tanzania: Homo erectus or Homo ergaster? Choice (B) is not correct.

Suppose Homo ergaster would have derived as much benefit from the master of fire as did the Homo erectus, or even more benefit. That fact, by itself, would imply nothing about which one of these species created those fires in Tanzania. Denying this doesn’t change the validity of the argument. Choice (C) is not correct.

Choice (D) is intriguing, because it may be true. Both Homo erectus and Homo ergaster evolved from Homo habilis, so it’s quite likely that the Homo habilis was the sole source of cultural knowledge for either of these species. BUT, we know that Homo erectus, presumably without the benefit of cultural knowledge about fire, was able to master fire. If Homo erectus did that, why couldn’t Homo ergaster? In other words, the limits of the cultural knowledge inherited does not necessarily set limits on what these human species could achieve. Therefore, we can draw no conclusion with respect to this argument. Choice (D) is not correct.

If Choice (E) were true, it would support the argument, but a supporting statement is not necessarily an assumption. We have to use the Negation Test. Suppose Homo ergaster was all over in Tanzania, before & during & after the time that those fires were created. Would that prove Homo ergaster started those fires? Not necessarily. It could still be true that both Homo ergaster and Homo erectus occupied that region, that only the latter had mastered fire, and therefore, that the later had to start those fires in Tanzania. Thus, we can deny choice and it doesn’t necessarily contradict the argument. Therefore, it is not an assumption. Choice (E) is not correct.

Answer = A
Critical Reasoning Questions: Boldface Structure[*]Critical Reasoning Questions: Paradox[*]Critical Reasoning Questions: Conclusion/Inference[/list]
Critical Reasoning questions challenge your thinking skills and ability to critically analyze arguments. They need great attention to detail and are immune to most shortcuts or gimmicks. Follow the above discussed tips to understand what is tested in these questions and master the GMAT CR.

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FROM Magoosh Blog: GMAT Word Problems: Introduction and Strategies.


You may love GMAT word problems or you may hate them, but you can’t get around them if you want to ace the GMAT Quant section. However, no matter what your feelings are about this problem type, Magoosh’s experts have put together everything you need to know (and practice!) in order to master GMAT word problems before you encounter them on test day.

Table of Contents
tips for plugging in numbers that you should use!

Here’s a quick summary of how to quick the best numbers for a particular problem:

  • Remember that the GMAT has a broad definition of “number” that goes beyond positive integers! Zero, fractions, and negatives are all included. Work on developing number sense to help select the best numbers in a given scenario.
  • For percent problems, think outside the box: GMAT test writers know lots of students pick 100. Try 500 or 1000 instead.
  • Don’t try to pick numbers for questions involving more than one percent increase or decrease.
  • Pay attention to units and convert them appropriately. This is particularly important in solutions and mixing problems!
  • Don’t pick 1 as a number—it has too many unique properties.
A separate case involving plugging in, rather than picking, numbers: When all the answer choices are numerical, one further strategy we have at our disposal is backsolving. Using this strategy, we can pick one answer, plug it into the problem, and see whether it works. If this choice is too big or too small, it guides us in what other answer choices to eliminate. Typically, we would start with answer choice (C), but if another answer choice is a particularly convenient choice, then we would start there.

error log of word problems you’ve answered wrong in your practice, then review it. As you go through, think about the following:

  • What concept or concepts was the question testing?
  • What was tricky about the wording of the question?
  • Were you already familiar with the methods used in the explanation video?
  • Once you watched the explanation video, could you explain how to solve the problem to somebody else?
Your answers to these questions can help you craft a better strategy for GMAT Math word problems, identifying exactly what you need to review to get better!



A Final Word on Word Problems
So, what is the trick to GMAT word problems? As you’ve seen in this post, there’s no one-size-fits-all trick—but there are plenty of strategies!

The strategies you’ve read about here can be used to take the given information and identify key words in a question. With them, you’ll be able to find everything from average speed to total distance traveled, from total time to total amount.

The key now is to put them into practice. Jot down these techniques or bookmark this post so you can come back as you continue your practice with GMAT word problems. You can also check out our posts on compound interest and Venn diagrams for more practice with GMAT word problems. Good luck!

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FROM Magoosh Blog: GMAT Practice Questions with Fractions and Decimals
Here are ten problems on fractions and decimals, some of which are quite challenging.  Remember, no calculator!





    (A) 0.1

    (B) 1

    (C) 10

    (D) 100

    (E) 1000






6)  Suppose you have access to a large vat of distilled water, several gallons large.  You have two precise measuring pipettes, one to measure exactly 1/3 of an ounce and one to measure exactly 1/4 of an ounce.  You can pour precisely measured amounts into a beaker, which initially is empty.  You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed.  Which of the following represents, in ounces,  a precise amount of distilled water you can transfer from the vat to the beaker?



    (A) I only

    (B) III only

    (C) I and III only

    (D) II and III only

    (E) I, II, and III




    (A) 440

    (B) 6,600

    (C) 13,200

    (D) 44,000

    (C) 132,000




    (A) 2

    (B) 4

    (C) 6

    (D) 8

    (E) 12
 

Fractions and Decimals
I have already written a few blogs that would be germane to these topics.

1) Fractions: some of the basic ideas of fractions

2) Terminating and Repeating Decimals: an assortment of decimal ideas

3) Advanced Factoring: some sophisticated techniques for factoring ungainly looking decimals

More advanced ideas will be discussed the explanations to these problems, below.



 

Solutions to Practice Problems
1) First, let’s separate out the denominators and simplify them.



and



We are adding the reciprocals of these two fractions:



Answer = (E).

2) Let’s handle the numerator and denominator separately to begin.  The number is the cube root of a decimal.  The first thing we have to recognize is that 4 cubed is 64, so the cube root of 64 is 4.  There are six total decimal places, so when we take a cube root, that will get divided by 3, down to only two decimal places.  Thus,



The denominator is a little easier.



Those are the two numbers we have to divide.  When divide decimals, we move both decimals an equal number of places to the right until the denominator is a whole number.   Here, after we set up the fraction, we will have to move both decimals four places to the right, because the denominator starts with four decimal point.



Answer = (D).

3) There are a few different ways to think about this.  First, I will multiply the entire inequality by positive 6.  This will leave the direction of the inequality unchanged, and I can multiply right through the absolute value signs.  This will eliminate any fractions.

|3y – 1| < 4

Well, the only way a thing can have an absolute value less than 4 is if it’s true value is between –4 and +4.  Thus

–4 < 3y – 1 < 4

Add one to each term.

–3 < 3y < 5

Now, divide by +3.  Because we are dividing by a positive, the direction of the inequalities stay the same.



So, y could be any positive or negative fraction between –1 and +1, so (B) & (C) & (D) are all allowed, and choice (E) is less than 5/3, so that’s also allowed.  The only one that is not allowed is (A), and that’s the answer.

4) Notice that all the denominators are multiples of 30, so factor out a factor of 1/30:



Answer = (B).

5) It’s actually better to change the decimals into fractions:



Answer = (B).

6) If you fill the 1/3 oz pipette and put this into the beaker.  Then use the other pipette to remove 1/4 oz from the beaker.  This 1/4 oz can be put back in the vat.



Thus, there would be 1/12 oz left in the beaker: that’s the amount that would have been transferred from the vat to the beaker.

If we repeat this same procedure, we will transfer another 1/12 oz from the vat to the beaker, and 2/12 = 1/6.  Therefore, we could transfer either 1/12 or 1/6 from the vat to the beaker.

There is no way to transfer 1/7 to the beaker.  No combination of arithmetic involving 1/3 and 1/4 will produce 1/7.

Answer = (C).

7) Let’s think about this is in stages.  First, call the entire denominator D; then (0.2)/D = 4.  From this, we must recognize that D must be 1/4 of 0.2, or D = 0.05.

Now, set that denominator equal to 0.05.

0.3 – x = 0.05

x = 0.3 – 0.05 = 0.25 = 1/4

Answer = (A).

8) Let’s make things easier by breaking this into two fraction.  First, let’s work with 3.3 divided by 0.015.  We will begin by sliding the decimals to the right a couple spaces:



Now, notice that the denominator is 3/2, so we will replace that decimal with the fraction:



That’s the first piece of the fraction.  Now, consider the rest:



Multiply the pieces

(220)*(200) = 44,000

Answer = (D).

9) For this one, we need to use some advanced factoring.  Notice that

0.9996 = 1 – 0.0004

Thus, we can express this as a difference of two squares, and use that to factor it



Now, consider that 0.98 = 1 – 0.02; then



When we subtract 1, we get 0.02, which equals 1/50.

Answer = (A).

10) Think of this in stages. Call the denominator D.  If 3/D = 12, then D must equal 1/4.

Now, look at the denominator. One minus thing equals 1/4, so that thing must equal 3/4.

Well, 6/c = 3/4, so c = 8.

Answer = (D).

 

If you’re looking to strengthen your Quant skills, Magoosh is here to help! Magoosh GMAT offers high-quality, affordable test prep to help you reach your score goals. Get access for a year with premium, or try us for free with a 1-week trial!

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FROM Magoosh Blog: Essential GMAT Algebra Formulas and Practice Questions


What are the most essential topics of algebra that you need to know to succeed in GMAT math? How many formulas and equations do you have to memorize? Why must we be tortured by all this math???

The good news is that it doesn’t take a huge amount of time or energy to master the basics. Most likely, you already have the fundamentals down.


Of course, it never hurts to review, so you might want to check out these first: Introduction to Algebra and FOIL on the GMAT: Simplifying and Expanding.[/*]
[/list]
 

This post is intended to help you gain the edge if you already have a solid foundation. By recognizing and taking advantage of some common algebraic expressions or patterns, and by remembering rather than memorizing.

Table of Contents
There is a common theme among the three items. In one way or another, they all have something to do with quadratic expressions. These tend to be more difficult to work with than linear equations, simply because the tools look more complicated.

Using the Patterns
The first two items in the list pertain to factoring—you can check out this post for more on that topic: Algebra on the GMAT: How to Factor.

The idea is that you can replace the expression on the left of the equals sign by the one on the right, and vice versa. This technique is often used in simplifying algebraic expressions. The practice problems below will also help you to understand when to use this strategy. The third item, the discriminant, is a powerful tool to help analyze the roots of quadratic equations without ever having to find the roots explicitly.


To see these concepts in action, check out our lesson videos on Factoring – Rational Expressions and Quadratic Equations.

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FROM Magoosh Blog: Variables in GMAT Answer Choices: Algebraic Approach vs. Numerical Approach
Fact: On GMAT Problem Solving, some of the prompts will state quantities in terms of variables, and then expect you to answer in terms of those variables.  Such questions are known as “variable in the answer choice” questions (or VICs in some circles).

Fact: There are two basic strategies you can use to solve these: (a) a full-on algebraic approach; or (b) plugging in numbers for the variables.

 

Which of these two approaches is better?  Well, we all know your Algebra Two teacher back in high school would have wanted you to pick the algebraic approach — perhaps that teacher even would have considered plugging in numbers a form of “cheating.”  BUT — this ain’t high school no more!  This is about GMAT, and as in the business world, the guiding principle for getting through the GMAT is: whatever works.

Which of the two approaches is better?  It depends entirely on you.  This is where you need to practice, trying each approach on questions like this, getting a feel for both approaches, so you develop a sense of which one works better with your style.

 

An Example Question
As an example, I’ll solve a new question from the OG 13 in both ways.  The question is Problem Solving #177 in the 13th edition:

 

177) Last year the price per share of Stock X increased by k percent and the earning per share increased by m percent, where k is greater than m.  By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

(A)

(B)

(C)

(D) 

(E)

 

This is a doozy of a question, because there are two variables in the question, and both play a role in the answer.  This question is only #177 of 230 PS questions, but it’s one of the hardest questions in that whole section.

 

Algebraic Approach
First, the approach that would have made your Algebra II teacher happy.  This will be hairy.  Let price per share be P, and earnings per share be E.  Then

original ratio =

new price per share =

new earnings per share =

new ratio = (new P)/(new E) =

 

Some comments.  Notice that to create the percent increases, I used multipliers.  If that’s unfamiliar, it’s a hugely important idea with which you need to acquaint yourself: see this post [https://magoosh.com/gmat/math/understanding-percents-on-the-gmat/].   Now, we need a percent increase from the original ratio to the new ratio.  This will be

 

Percent increase = 



 

Cancel the factor of P/E everywhere in the fraction

 



 

Find a common denominator inside the parentheses.

 



 



 



 

This matches exactly answer D, the correct answer.

 

Numerical Approach
We need several numbers, which we will pick for ease of calculation rather than for realism.  First, say price per share P = 100 (many common stocks are in the ballpark of $100/share) and say that earnings per share is also E = 100 (that’s the part that is unrealistic, but it makes for an easy calculation).  The original ratio, P/E = 100/100 = 1.

We need k > m, so let’s say k = 50 and m = 20.  Then the new P is 150, the new E is 120, and the new ratio is 150/120 = 15/12 = 5/4.

The change from 1 to 5/4 involves adding a quarter, and a quarter is 25%, so it’s a 25% increase in the ratio.  Now, the question is: with values of k = 50 and m = 20, which answer choice gives the correct answer of 25?  Before we plug in, we don’t know — it’s possible the values we pick work for two answers: in that case, we would eliminate the cases which didn’t work, then pick new values, and repeat, but only checking the cases that worked the first time.

So, the answers:

 

(A) k/m % = 50/20% does not equal 25%!  Out.

 

(B) (k – m)% = (50 – 20)% = 30% Out.

 

(C) 100*(k – m)/(100 + k) % = (100*30)/150 = 3000/150 = 20% Out.

 

(D) 100*(k – m)/(100 + m) % = (100*30)/120 = 3000/120 = 25% Works.

 

(E) 100*(k – m)/(100 + k + m) % = (100*30)/170 = 3000/170 = 300/17 = not a whole number, so it certainly doesn’t equal 25. Out.

 

We got lucky!  One choice for the variables was enough to eliminate four of the five, leaving only the correct answer D.  In general, if you don’t pick the most obvious choices (k = 200 & m = 100, or k = 100 & m = 50), then you are likely to eliminate four answer choices on your first pick of numbers.  That’s one of many reasons it’s an excellent idea to pick less-than-perfectly-obvious numbers when you are taking a numerical approach to a problem like this.

Here’s another question with variables in the answer choices on which you can practice: http://gmat.magoosh.com/questions/325

If you sign up for the Magoosh product, you will get access to this important lesson on problems with variables in the answer choices: http://gmat.magoosh.com/lessons/283-variables-in-answer-choices

 

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FROM Magoosh Blog: GMAT Probability: Difficult Dice Questions
Dice problems aren’t too common on GMAT quant. As for the exact probability of getting a dice problem is something only privy to those over at GMAC.

While it is a good idea to know your dice basics, doing so will only help you in the case of an easy dice problem. And one thing is for sure – if you are looking to break a 705 on the GMAT the probability of an easy dice problem (if you end up getting a dice problem) is very, very low.

Below are three excruciatingly difficult dice problems. They will pop up only if you are heading towards a high score. For those still brushing up on their math fundamental don’t waste time on such challenge questions.

GMAT Dice Probability Practice Questions
1. What is the probability of rolling the same number exactly three times with five six-sided dice?

  • 1/5
  • 5/18
  • 35/216
  • 125/648
  • 225/1296
 

2. What is the probability of rolling three six-sided dice, and getting a different number on each die?

  • 1/12
  • 1/3
  • 4/9
  • 5/9
  • 7/18
 

3. A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?

  •  7/108
  • 5/54
  • 1/9
  • 2/17
  • 1/4

Answer Explanations:
Question 1
Rolling any number on a dice three times in a row is equal to the number of throws
, where 3 represents the number of throws and 6 is the number of different ways to get three of the same number (e.g. 1, 1, 1  2, 2, 2  3, 3, 3…).

Next we have to use the combinations formula to determine how many ways three out of five can be the same.
. We want to multiply this number to

We are not finished yet – there is one little twist to the problem. The question says “exactly three times.” Meaning we have to discount all the instances in which we roll the same number four times and those instance in which we roll the same number five times.

One way to do so is by multiplying by the probability that the fourth and fifth dice will NOT land on the same number as the three dice. Because there are five other possibilities on dice that will not compromise “exactly three numbers” we can multiply by

Finally this gives us

Question 2
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.

6 x 5 x 4 = 120 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6 = 216).

120/216 = 5/9

Question 3
Perhaps the hardest of the bunch, this question requires that we find a solution that doesn’t take much longer than 2 minutes. A quick way – or at least relatively quick way – is to determine the number of instances in which our roll of one die will yield more than two die. Intuitively, this is a good place to start because the number of instances in which rolling a great number with one die than with two is much smaller than vice versa.

The only way to roll higher on one die is if the magicians rolls between 2 and 5, inclusive, with two dice. Were he to roll a six with two dice than there is no way he could eclipse that number by rolling one die.

Below is the probability of rolling a certain number with two dice.

‘2’ – 1/36

‘3’ – 2/36

‘4’ – 3/36

‘5’-  4/36

Now the only numbers a magician can roll with the one die and win is between 3 and 6, inclusive. The chances of rolling any are always 1/6.

Next, we have to combine the probability distribution relating to two dice with that relating to the one.

The chances of a magician rolling any given number with one die are 1/6. So let’s start with the lowest number he can roll: a ‘3.’ To win with this roll, he will have to roll a ‘2’ with two dice, the odds of which are 1/36. So
.

So the chances of him rolling a ‘3’ with one die and winning are 1/216.

Let’s repeat this logic for the next roll, ‘4.’ Chances of rolling are 1/6. Only way a ‘4’ wins is if he rolls a ‘2’ or a ‘3’ with two dice.

Odds of rolling a ‘2’ with two dice  + odds of rolling a ‘3’ with two dice =
. Combine this with the odds of rolling a ‘4’ ( which is 1/6):
.

If he rolls a ‘5’ with one die, he can win if he rolls a ‘4’ with two dice, the probability is 3/36. He can also win if he rolls a ‘2’ or a ‘3’ with two dice, the number outcomes we just found: 3/36. So we add

Next, if he rolls a ‘6’ on one die, he can beat ‘2’ through ‘5’ with the two dice. Number of ways to roll a ‘5’ = 4/36. Combining this with the odds of rolling a ‘6’ on one die with the odds or rolling ‘2’, ‘3’, ‘4’, or ‘5’ with the two dice we get: 10/216.

You may be wondering why I left the denominator as 216. Well, this allows us to add up all the instances he can possibly win:


 (Answer B)

 

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FROM Magoosh Blog: GMAT Probability Rules
[img]https://magoosh.com/gmat/files/2019/09/GMAT-Probability-Post.png[/img]

For those of you who are ready to take on GMAT probability, here is the absolute bare minimum you need to know to successfully attack probability calculations on the GMAT:

The Simplistic Probability Rules
[b]“AND” means MULTIPLY[/b]
[b]“OR” means ADD[/b]
Is that the entire story? Well, no. But! If you can’t remember, or don’t understand anything else about probability, at least hang on to those two bare-bones rules. Just knowing how to translate “and” vs. “or” will put you ahead of the game. As you’ll see with the practice problems later on in this post, knowing these rules is enough to solve some GMAT problems. Of course, the more complex the problem, the more you’ll need to understand the limitations of the most simplistic rules. Therefore, we need to discuss a few distinctions:

Mutually Exclusive
One important idea in probability is mutually exclusive (a.k.a. “disjoint”). Two events are mutually exclusive if they both can’t happen at the same time. For example, on a single die roll, the six numbers on the die are mutually exclusive. That is, it is absolutely impossible to have them both happen at the same time.   If you roll one die, you can’t simultaneously get, say, both a 3 and a 5.  Suppose we are picking random people and classifying them by their current age.  In this process, being in the category “teenager” and being in the category “senior citizen” are mutually exclusive: There is no one we could pick who is simultaneously in both categories. 

When the events [b]A[/b] and [b]B[/b] are [b]mutually exclusive[/b], then we can use the [b]simplified OR rule[/b]:

[b]P(A or B) = P(A) + P(B)[/b]

However, if events A and B are [b]not mutually exclusive[/b], then we have to use the [b]generalized OR rule[/b]:

[b]P(A or B) = P(A) + P(B) – P(A and B)[/b]

For events that are [b]not[/b] mutually exclusive, we need to subtract the overlap.  The events of region “A and B” are included in both region A and region B, so if we simply added those two regions, the overlap would be counted twice. To avoid that, we need to subtract, ensuring that all events are only counted once.

Independent Events
Two events are independent if the occurrence of one event has absolutely no influence on whether the other event occurs.  In other words, knowing about the outcome of one event gives absolutely no information about how the other event will turn out.   For example, if I roll two ordinary dice, the outcome of each die is independent of the other die.  If I tell you I rolled two dice, and the first die was a 4, then knowing that gives you no clue about what the number on the other die might be.

Word to the wise! We have to pay attention to the details of the scenario. For instance, if I shuffle a deck of cards, draw one, replace it, re-shuffle, and draw another, then the two cards are independent.  BUT, if I shuffle the deck, draw one card, and then without replacement draw a second card, then they are not independent. If the first card is the 7 of Hearts, then it is less likely that the second card would be either a 7 or a Heart, because there are fewer of those options among the remaining 51 cards.

If events [b]A[/b] and [b]B[/b] are [b]independent[/b], then we can use the [b]simplified AND rule[/b]:

[b]P(A and B) = P(A)*P(B)[/b]

However, if events A and B are [b]not[/b] [b]independent[/b], then things get complicated.  Technically, the “generalized AND rule” formula would involve a concept known as “conditional probability,” which would lead into realms of probability theory that are tested far less frequently on the GMAT. We will get to more advanced concepts later on in this post. At this point, let’s practice the basics.

Simplistic Probability Practice Questions
The scenario below is relevant to questions #1-#3.

There are two sets of letters, and you are going to pick exactly one letter from each set.

Set #1 = {A, B, C, D, E}

Set #2 = {K, L, M, N, O, P}

1) What is the probability of picking a C and an M?

[list]
(A) 1/30

(B) 1/15

(C) 1/6

(D) 1/5

(E) 1/3
[/list]
2) What is the probability of picking a C or an M?

[list]
(A) 1/30

(B) 1/15

(C) 1/6

(D) 1/5

(E) 1/3
[/list]
3) What is the probability of picking two vowels?

[list]
(A) 1/30

(B) 1/15

(C) 1/6

(D) 1/5

(E) 1/3
[/list]
_____________________________________________________________________

4) In a certain corporation, there are 300 part-time employees and 100 full-time employees.  It is known that 20% of the part-time employees have advanced degrees and 40% of the full-time have advanced degrees.  If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree and is a full-time employee?

[list]
(A) 1/20

(B) 1/10

(C) 1/5

(D) 2/5

(E) 3/4
[/list]
5) In a certain corporation, there are 300 part-time employees and 100 full-time employees.  It is known that 20% of the part-time employees have advanced degrees and 40% of the full-time have advanced degrees.  If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is a full-time employee?

[list]
(A) 1/20

(B) 1/10

(C) 1/5

(D) 2/5

(E) 3/4
[/list]
[b]Looking for solutions?[/b] Scroll to the end of the post, where you’ll find the solutions to both the simplistic and advanced question sets.

Advanced Probability Rules
Conditional Probability
Because conditional probability does pop up from time to time on the GMAT, here’s a quick overview.

For conditional probability, the notation we use is P(A|B). Event A is the main focus: we are interested whether or not A occurs. Event B is some kind of condition we impose: the idea is, we will pretend that we live in a world in which Event B is always true — under those conditions, what is the probability of A? P(A|B) is a “conditional probability”, a probability when we impose the condition of B. The notation P(A|B) is read “the probability of A, given B.”

Here are a few examples. Suppose that

A = on a given day in Berkeley, CA, it rains

B = on a given day in Berkeley, CA, there are no clouds in the sky.

Here P(A) would be the probability that in Berkeley, CA we get rain on a randomly selected day; that would be approximately 0.10 or 0.15. By contrast, if we impose the condition “no clouds”, then the conditional probability, P(A|B), would have to be zero: how could it possibly rain when there are no clouds? This is an example of a condition lowering a probability. Of course, there are other conditions that could raise the probability of it raining in Berkeley.

The Generalized AND Rule
Now that we have discussed conditional probability, we can discuss the generalized AND rule. Again, not feeling ready for these advanced topics? No worries, skip on down to the basic probability practice questions. If you’re ready to level-up, here we go:

If events A and B are two general events, not mutually exclusive, not independent, then, as a general rule:

[b]P(A and B) = P(A)*P(B|A)[/b]

P(A and B) = P(B)*P(A|B)[/b]

Either one of these is the generalized AND rule. Notice that AND still means multiply, though what we multiply here is a little different from what was multiplied in the case with independent events.

For example, suppose we are going to pick two cards from a full 52-card deck, without replacement, and we want to know the probability of picking two heart-cards. The phrase “without replacement” means when we pick the first card, we put it aside and do not return it to the deck, so that the second card is picked from a deck of only 51 cards. That changes the probability. The words “without replacement” always means the choices are NOT independent, because the outcome of the first choice has a big influence on the outcome of subsequent choices. For this example, let

A = first choice is a heart-card

B = second choice is a heart-card

There are four suits in a full deck, and each suit is equally represented, so P(A) = 1/4. Let’s think about P(B|A). If the first card was a heart-card and it was not replaced, that means the second choice is made from a deck of 51 cards that has 13 of the other three suits but only 12 heart-cards. Thus, P(B|A) = 12/51 = 4/17, and P(A and B) = (1/4)*(4/17) = 1/17

The generalized AND rule is often used in sequential tasks such as this, in which there are earlier choices or trials, and the outcomes of these have various effects on later choices or trials. The generalized AND rule is most often not applicable in a more side-by-side choice, in which all the choices are available at the outset.

If you are hankering for more advanced concepts, here are a couple other posts to check out:

1) [url=https://magoosh.com/gmat/gmat-math-the-probability-at-least-question/]The Probability “At Least” Question[/url]

2) [url=https://magoosh.com/gmat/gmat-probability-and-counting-techniques/]Probability and Counting Techniques[/url]

Advanced Probability Questions
In the following probability problems, problems #1-3 function as a set, problems #4-5 are another set, and problems #6-7 are yet another set.  The scenarios are all similar in a set, and the answer choices for those problems in the same set are the same.  What is going on there?  Do all questions in the same set have the same answer? Do all have different answers?  What is happening?

1) In a certain game, you perform three tasks.  You flip a quarter, and success would be heads.  You roll a single die, and success would be a six.  You pick a card from a full playing-card deck, and success would be picking a spades card.   If any of these task are successful, then you win the game.  What is the probability of winning?

[url=https://magoosh.com/gmat/files/2013/12/gp_img1.png][img]https://magoosh.com/gmat/files/2013/12/gp_img1.png[/img][/url]

2) In a certain game, you perform three tasks sequentially.  First, you flip quarter, and if you get heads you win the game. If you get tails, then you move to the second task. The second task is rolling a single die.  If you roll a six, you win the game.  If you roll anything other than a six on the second task, you move to the third task: drawing a card from a full playing-card deck.  If you pick a spades card you win the game, and otherwise you lose the game.  What is the probability of winning?

[url=https://magoosh.com/gmat/files/2013/12/gp_img2.png][img]https://magoosh.com/gmat/files/2013/12/gp_img2.png[/img][/url]

3) In a certain game, you perform three tasks.  You flip a quarter, and success would be heads.  You roll a single die, and success would be a six.  You pick a card from a full playing-card deck, and success would be picking a spades card.   If exactly one of these three tasks is successful, then you win the game.  What is the probability of winning?

[url=https://magoosh.com/gmat/files/2013/12/gp_img3.png][img]https://magoosh.com/gmat/files/2013/12/gp_img3.png[/img][/url][url=https://magoosh.com/gmat/files/2013/12/line.png][img]https://magoosh.com/gmat/files/2013/12/line.png[/img][/url]

The following information accompanies questions 4-5

Johnson has a corporate proposal.  The probability that vice-president Adams will approve the proposal is 0.7.  The probability that vice-president Baker will approve the proposal is 0.5.  The probability that vice-president Corfu will approve the proposal is 0.4.  The approvals of the three VPs are entirely independent of one another.

4) Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding.  What is the probability that Johnson’s proposal is funded?

(A) 0.14

(B) 0.26

(C) 0.49

(D) 0.55

(E) 0.86

5) Suppose Johnson must get the approval of at least two of the three VPs to win funding.  What is the probability that Johnson’s proposal is funded?

(A) 0.14

(B) 0.26

(C) 0.49

(D) 0.55

(E) 0.86

[url=https://magoosh.com/gmat/files/2013/12/line.png][img]https://magoosh.com/gmat/files/2013/12/line.png[/img][/url]

The following information accompanies questions 6-7

Johnson has a corporate proposal.  The probability that vice-president Adams will approve the proposal is 0.6.  If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.8.  If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3.

6)  What is the probability that one of the two VPs, but not the other, approves Johnson’s proposal?

(A) 0.12

(B) 0.24

(C) 0.28

(D) 0.48

(E) 0.72

7)  What is the probability that at least one of the two VPs, approves Johnson’s proposal?

(A) 0.12

(B) 0.24

(C) 0.28

(D) 0.48

(E) 0.72

Practice Question Solutions
Simplistic Probability Solutions
1) Whatever we pick from the first set is independent with whatever we pick from the second set, so we can use the simplified AND rule.

P(first pick = C) = 1/5

P(second pick = M) = 1/6

P(C and M) = P(C)*P(M) = (1/5)*(1/6) = 1/30

Answer = [b]A[/b]

2) Picking an M is not disjoint with picking a C — they both could happen on the same round of the game.   We have to use the generalized OR rule for this:

P(C or M) = P(C) + P(M) – P(C and M)

Fortunately, we know the first two, and we calculated the value of the third term already in #1.

P(C or M) = P(C) + P(M) – P(C and M)

[url=https://magoosh.com/gmat/files/2012/12/pp_img11.png][img]https://magoosh.com/gmat/files/2012/12/pp_img11.png[/img][/url]

Answer = [b]E[/b]

3) On the first pick, two of the five letters are vowels — A & E — so the probability of picking a vowel on the first pick is 2/5.   On the second pick, only one letter out of the six is a vowel — O — so the probability of picking a vowel on the second pick is 1/6.  The two picks are independent: what one selects from one set has absolutely no bearing on what one picks from the other set.   Therefore, we can use the generalized AND rule.

P(two vowels) = P(vowel on first pick)*P(vowel on second pick) =(2/5)*(1/6) = 2/30 = 1/15

Answer = [b]B[/b]

4) Here we have an AND question, and the parameters — full-time and advanced degree — are not independent.  If I tell you the status of a certain employee, then that gives me information about how likely it is that this employee has an advanced degree.   One parameter gives information about the other, which means they are not independent.  Therefore, we cannot use the simplified AND rule.  Fortunately, it is relatively easy here to calculate everything directly.

There are 100 full-time employees, and we know 40% of them have advanced degrees, so there are 40 employees who both are full-time and have an advanced degree.  That’s the number of employees in the AND region.  Well, there are 400 employees altogether.  Of these 400 total employees, the probability of picking someone in this AND region is

P = 40/400 = 1/10

Answer = [b]B[/b]

5)  In this corporation, there are 400 total employees.  There are 100 full-time.  Of the 300 part-time, 20% have advanced degrees —-10% of 300 must be 30, so 20% of 300 must be 60.  Add the full-time employees and the part-time employees with advanced degrees: 100 + 60 = 160.   This is the OR region, full set of individuals that satisfy the condition “has an advanced degree or is full-time.”  Of the 400 employees, what’s the probability of picking one of the 160 in this particular group?

P = 160/400 = 16/40 = 4/10 = 2/5

Answer = [b]D[/b]

Advanced Probability Solutions
1) In this scenario, winning combinations would include success on any one task as well as any combination of two or three successes.  In other words, there are several cases that constitute the winning combinations.  By contrast, the only way to lose the game would be unsuccessful at all three tasks.  Let’s use the [b]complement rule[/b].

P(lose game) = P(quarter = T AND dice ≠ 6 AND card ≠ spades)

= (1/2)*(5/6)*(3/4) = 5/16

P(win game) = 1 – P(lose game) = 1 – (5/16) = 11/16

Answer = [b](D)[/b]

2) In this scenario, there are several routes that would lead to winning the game.  The only route that leads to losing the game is the route in which all three tasks are unsuccessful.  We can do this precisely as we did the previous problem.

P(lose game) = P(quarter = T AND dice ≠ 6 AND card ≠ spades)

= (1/2)*(5/6)*(3/4) = 5/16

P(win game) = 1 – P(lose game) = 1 – (5/16) = 11/16

Answer = [b](D)[/b]

3) This is very tricky.  We have to think of three cases.

Case One: success with coin, no success with die or card

P(coin = H AND die ≠ 6 AND card ≠ spade) = (1/2)*(5/6)*(3/4) = 15/48

Case Two: success with die, no success with coin or card

P(coin = T AND die = 6 AND card ≠ spade) = (1/2)*(1/6)*(3/4) = 3/48

Case Three: success with card, no success with die or coin

P(coin = T AND die ≠ 6 AND card = spade) = (1/2)*(5/6)*(1/4) = 5/48

The winning scenario could be Case One OR Case Two OR Case Three.  Since these are joined by OR statements and are mutually exclusive, we simply add the probabilities.

[url=https://magoosh.com/gmat/files/2013/12/gp_img5.png][img]https://magoosh.com/gmat/files/2013/12/gp_img5.png[/img][/url]

Answer = [b](E)[/b]

4) We will use the abbreviation A = VP Adams approves, B = VP Baker approves, and C = VP Corfu approves.

P(funding) = P(A and (B or C)) = P(A)*P(B or C)

We can multiply because everything is independent of everything else.  First look at P(B or C).  These are not mutually exclusive, so we need to use the generalized OR rule:

P(B or C) = P(B) + P(C) – P(B and C)

Because B & C are independent, we can multiply to find P(A and B)

P(B or C) = (0.5) + (0.4) – (0.5)*(0.4) = 0.9 – 0.2 = 0.7

Now, multiply by P(A)

P(funding) = P(A)*P(B or C) = (0.7)*(0.7) = 0.49

Answer = [b](C)[/b]

5) For this one, we have to consider four different cases

P(A and B and (not C)) = (0.7)*(0.5)*(0.6) = 0.21

P(A and (not B) and C) = (0.7)*(0.5)*(0.4) = 0.14

P((not A) and B and C) = (0.3)*(0.5)*(0.4) = 0.06

P(A and B and C) = (0.7)*(0.5)*(0.4) = 0.14

These four are mutually exclusive and are joined by OR, so we add them.

P(funding) = 0.21 + 0.14 + 0.06 + 0.14 = 0.55

Answer = [b](D)[/b]

6) We will use the abbreviation A = VP Adams approves and B = VP Baker approves.  We will consider two cases:

Case #1: Adams approves and not Baker

P(A and not B) = P(A)*P(not B|A) = (0.6)*(0.2) = 0.12

Case #2: Baker approves and not Adams

P(not A and B) = P(not A)*P(B|not A) = (0.4)*(0.3) = 0.12

These two cases are mutually exclusive and joined by OR, we add them.

P(only one VP approves) = 0.12 + 0.12 = 0.24

Answer = [b](B)[/b]

7) Here, the combinations (A and not B), (not A and B), and (A and B) all lead to approval of the proposal.  The only one that doesn’t is the complement (not A and not B).

P(not A and not B) = P(not A)*P(not B|not A) = (0.4)*(0.7) = 0.28

P(at least one) = 1 – P(not A and not B) = 1 – 0.28 = 0.72

Answer = [b](E)[/b]

Summary
If you understand everything in this post, you are a GMAT Probability pro. If some of the concepts feel a bit challenging, you are not alone. Probability questions are a type that a lot GMAT test-takers struggle with. But! Keep practicing, and you will find that these, too, will become easier.

The post [url=https://magoosh.com/gmat/gmat-probability-rules/]GMAT Probability Rules[/url] appeared first on [url=https://magoosh.com/gmat]Magoosh Blog — GMAT® Exam[/url].
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FROM Magoosh Blog: How Much Does the GMAT Cost? A Guide to GMAT Exam Fees


Getting into and going to graduate school is pricey, and there’s no denying that the GMAT cost of $275 is an added expense. GMAT exam fees are hefty, and more expensive than many similar standardized exams (except the MCAT…). Furthermore, the actual GMAT cost is not the only fee you have to consider. Most test-takers purchase some sort of practice materials, and many students even take the exam more than once. No doubt about it, paying GMAT exam fees will impact your wallet. In this post, we’ll go over what fees you can expect to pay and how to minimize the cost of taking the GMAT.

An Overview of GMAT Exam Fees
Before we get into any more detail, let’s look at how much the GMAT might cost you. (NOTE: This table applies to most of the world, but not to Europe. In Europe, GMAT scheduling and other GMAT fees can vary a little bit from the costs in the table below.) We split the fees in this table by in-person (taken at a testing center) and online, the latter which costs more.

In-Person (Test Center)
Online

Scheduling fee (U.S. and Canada)
$275
$300

Scheduling fee (US Overseas Territories, some other countries)
$250
$275

Additional score report
$35
$35

Rescheduling fee (more than 60 days out)
$55
$60

Rescheduling fee (15-60 days out)
$110
$120

Rescheduling fee (within 14 days of the exam)
$165
$180

Cancellation refund (15-60 days out)
$110 refund
$120 refund

Cancellation refund (15-60 days out)
$80 refund
$90 refund

Cancellation refund (within 14 days of the exam)
$55 refund
$60 refund

With that in mind, let’s take a look at some of these GMAT costs in more detail. Skip ahead to a section by selecting a GMAT cost or GMAT score report section from the navigation table below, or keep scrolling down to review all information. For the remainder of this post, we will show the test center price first, then the online price (as in-person/online).

the official GMAT Exam Payment page for more information.

 

Note, however, that if you choose to pay by phone you will be charged an additional $10 or so (again, fees can vary in Europe, especially when a currency other than USD is in play). So, if you have easy access to the internet, register online!

GMAT prep book or online test prep could cost you less than $150.

To maximize your prep with video lessons, practice questions, tests, and more to help you boost your score, we recommend checking out Magoosh GMAT. Try us for free with a 1-week trial!

For high-quality free practice, you can also check out:

[list]
[*]GMATPrep Software from GMAC[/*]
[*]Advice from Online Forums[/*]
[*]You can also check out the get into business school, after all. And that’s very expensive!

Since B-school itself will be pricey, you might want to consider this when budgeting in your GMAT cost. If you’re concerned about expenses, you might consider planning to avoid a rescheduling fee or a retake. In addition, be aware that GMAT fee waivers may be available.

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FROM Magoosh Blog: GMAT for Non-Native English Speakers


Preparing for the GMAT exam can be a daunting task, especially if English is not your first language. The verbal section, in particular, poses unique challenges that require a strategic approach and diligent practice. If you are looking for advice on how to modify or supplement your Magoosh Study Schedule, you’ve come to the right place. If you’re just looking for advice on how to approach the GMAT as a Non-native English speaker, you’ve also come to the right place. Read on for tips and strategies that will help you excel in preparing for verbal part of the exam.

The Most Important GMAT Tip for Non-Native English Speakers:

The number one thing you can do to improve your verbal performance on the GMAT is to read English as much as possible. There is simply no better way to improve than through A LOT of practice. The upside to all this reading is that you will not only boost your vocabulary, but also your comprehension skills — your ability to digest meaning and decipher the author’s intent. This is a crucial skill for the GMAT verbal section.

Recommended Practice for Non-Native English Speakers:

You should read for at least 30 minutes per day. If you are really struggling with GMAT Verbal and can afford the time, make it at least one hour per day.

We understand that reading for 30 minutes to one hour each day is not a small task. You might be wondering how to find the time, especially if you’re trying to diligently follow each and every item in your Magoosh Study Schedule–we know each day is already packed. But! You don’t have to follow the study schedule to a T. The schedules were designed to be modified based on an individual’s strengths and weaknesses. If, as a non-native English speaker or someone weaker in verbal, it’s in your best interest to read for an hour (or more) each day as well as have time to record and review any unfamiliar vocabulary, you should feel free to modify the demands of the schedule in whatever way best suits your GMAT success.

Modifying Your GMAT Study Schedule:

Let’s say that you are already really strong in Quantitative Reasoning (QR) concepts. Well, if that’s the case, at the beginning of each week, look through the QR content to see whether you already know the content of a lesson or just need to lightly review it. If you’re confident you know the concepts, you could either skip those lessons completely or maybe just skim through any for which you only need a brief refresher. All the time that you don’t need to devote to QR can then be applied to reading and more GMAT verbal practice.

Please Note: We recommend that you don’t completely skip any given lesson’s associated practice questions because your performance on those questions will reveal any unexpected weaknesses and lessons that you should, in fact, review more fully.

You Cannot Skip or Skim any GMAT Topics:

If you find that it’s not in your best interest to skip any of the lessons in your schedule, you still need to do your best to practice reading as much as possible, especially if you are a non-native English speaker who finds the vocabulary and sentence complexity of GMAT verbal difficult to navigate. Unfortunately, the best way to see a significant improvement in your verbal score is to become as comfortable as possible with reading higher-level English texts, and that takes time. Be honest with yourself. If you cannot add time to practice reading each day as well as knock out all the lessons and practice in the schedule, at the bare minimum, can you fit a longer reading session into a sixth or seventh day?

If there’s simply no way you can incorporate the reading you need to do to help you improve your verbal score into your current study schedule, you might need to consider increasing the total amount of time you’ve allocated to studying for the GMAT. Many non-native English speakers give themselves up to a year or more to prepare, specifically because of the need to be as comfortable as possible with the English complexity they’ll encounter on the GMAT.

What to Read to Prepare for the GMAT:

It’s important to read materials that are similar to what you’ll see come test day. Consider such venerated publications as The New York Times, The New Yorker, The Economist, and Arts & Letters Daily. Take a look at our full list of recommended periodicals. Or, if you prefer books, check out our recommended fiction & non-fiction (this list is written for the GRE, but all the picks would suit the GMAT as well).

How to Read to Prepare for the GMAT:

  • Active Reading: Practice reading actively by summarizing paragraphs, identifying main ideas, and noting key details. To delve deeper into this crucial skill, check out our post dedicated to active reading.
  • Annotation: Make notes and highlight key points while reading to improve retention and understanding.
  • Summarization: After reading a passage, write a brief summary in your own words to ensure comprehension.
  • Vocabulary Building: Use your most effective method (flashcards often work well) to record any and all words that are new to you. Part of your GMAT study should be to review these words often.
  • Translation Tools: Use them to support your efforts but always remember that there is no escaping the need to enhance your English vocabulary if you want to improve your GMAT verbal score. We’ve highlighted Google’s translation tool here:
[img]https://magoosh.com/gmat/files/2024/06/Screenshot-2024-06-06-at-2.16.29 PM-600x348.png[/img]

Final Thoughts:

It will not be easy to catch up with native speakers on an exam like the GMAT. Preparing for the verbal section of the GMAT exam as a non-native English speaker requires dedication, practice, and strategic planning. Magoosh is here to help! Hopefully, you now feel empowered to modify your study schedule in a way that will help you significantly enhance your performance. And, remember, be kind to yourself. Improving in verbal can feel like an uphill battle but maintaining a consistent effort and a positive mindset are key to achieving your desired score.

Good luck!

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FROM Magoosh Blog: GMAT Math: The Probability “At Least” Question
[b]This post was updated in 2024 for the new GMAT.[/b]

In the first post in this series, I spoke about the AND and the OR [url=https://magoosh.com/gmat/gmat-probability/]probability rules[/url].  Now, we will focus on probability questions involving the “at least” probability.

[img]https://magoosh.com/gmat/files/2012/12/GMAT-Probability.jpg[/img]

The complement rule
There is a very simple and very important rule relating P(A) and P(not A), linking the probability of any event happening with the probability of that same event not happening.  For any well-defined event, it’s 100% true that either the event happens or it doesn’t happen.

The GMAT will not ask you probability question about bizarre events in which, for example, you can’t tell whether or not the event happened, or complex events which could, in some sense, both happen and not happen.  For any event A in a probability question on the GMAT, the two scenarios “A happens” and “A doesn’t happen” exhaust the possibilities that could take place.

With certainty, we can say: one of those two will occur.  In other words:

P(A [b]OR[/b] not A) = 1

Having a probability of 1 means guaranteed certainty.  Obviously, for a variety of deep logical reasons, the events “A” and “not A” are disjoint and have no overlap.  The OR rule, discussed in the last post, implies:

P(A) + P(not A) = 1

Subtract the first term to isolate P(not A).

[b]P(not A) = 1 – P(A)[/b]

 

[list]
[*]That is known in probability as the [b]complement rule[/b], because the probabilistic region in which an event doesn’t occur complements the region in which it does occur.[/*]

[/list]
This is a crucial idea in general, for all GMAT probability questions, and one that will be very important in solving “at least” questions in particular.

The complement of “at least” statements
Suppose event A is a statement involving words “at least”—how would we state what constituted “not A“?  In other words, how do we negate an “at least” statement?

Let’s be concrete.  Suppose there is some event that involves just two outcomes: success and failure.  The event could be, for example, making a basketball free throw, or flipping a coin and getting heads.  Now, suppose we have a “contest” involving ten of these events in a row, and we are counting the number of successes in these ten trials. 

Let A be the event defined as: A = “there are at least 4 successes in these ten trials.”  What outcomes would constitute “not A“?  Well, let’s think about it.  In ten trials, one could get zero successes, exactly one success, exactly two successes, all the way up to ten successes.  There are eleven possible outcomes, the numbers from 0 – 10, for the number of successes one could get in 10 trials.

Consider the following: number of possible successes in ten trials:

[b] 0 1 2 3 4 5 6 7 8 9 10 [/b]

The purple numbers are the members of A, the members of “at least 4 successes” in ten trials.  Therefore, the green numbers are the complement space, the region of “not A.”  In words, how would we describe the conditions that land you in the green region?  We would say: “not A” = “three or fewer success” in ten trials.   The negation, the opposite, of “at least four” is “three or fewer.”

Abstracting from this, the negation or opposite of “at least n” is the condition “(n – 1) or fewer.”

[list]
[*]One particularly interesting case of this is n = 1:[b] the negation or opposite of “at least one” is “none.”[/b][/*]
[/list]
That last statement is a hugely important idea, arguably the key to solving most of the “at least” questions you will see on the GMAT.

Solving an “at least” question
The big idea for any “at least” question on the GMAT is:

[list]
[*][b]It is always easier to figure out the complement probability[/b].[/*]
[/list]


For example, in the above scenario of ten trials of some sort, calculating “at least 4” directly would involve seven different calculations (for the cases from 4 to 10), whereas the calculation of “three or fewer” would involve only four separate calculations (for the cases from 0 to 3).

In the extreme—and extremely common—case of “the probability of at least one”, the direct approach would involve a calculation for almost case, but the complement calculation simply involves calculating the probability for the “none” case, and then subtracting from one.

P(not A) = 1 – P(A)

P(at least one success) = 1 – P(no successes)

This is one of the most powerful time-saving shortcuts on the entire GMAT.

 

An example calculation
Consider the following simple question.

Two dice are rolled.  What is the probability of at least one of the dice rolling a 6?

It turns out, calculating that directly would involve a relatively long calculation — the probability of exactly one 6, on either die, and the rare probability of both coming up 6’s.  That calculation easily could take several minutes.

Instead, we will use the shortcut defined above:

P(not A) = 1 – P(A)

P(at least one 6) = 1 – P(no 6’s)

What’s the probability of both dice coming up no 6’s?  Well, first, let’s consider one die. The probability of rolling a 6 is 1/6, so the probability of rolling something other than 6 (“not 6”) is 5/6.

P(two rolls, no 6’s) = P(“not 6” on dice #1 AND “not 6” on dice #2)

As we found in the previous post, the word AND means multiply.  (Clearly, the outcome of each die is independent of the other).   Thus:

P(two rolls, no 6’s) =(5/6)*(5/6) = 25/36

P(at least one 6) = 1 – P(no 6’s) = 1 – 25/36 = [b]11/36[/b]

What could have been a long calculation becomes remarkably straightforward by means of this shortcut. This can be an enormous time-saver on the GMAT!

Practice
Now that you’ve read this post, take shot at these three practice questions before reading the answers and explanations below.

Set #1 = {A, B, C, D, E}

Set #2 = {K, L, M, N, O, P}

[*]There are these two sets of letters, and you are going to pick exactly one letter from each set.  What is the probability of at least one vowel being picked?

[*]1/6[/*]
[*]1/3[/*]
[*]1/2[/*]
[*]2/3[/*]
[*]5/6[/*]
[/list]
[/*]
[/list]

Show answer and explanation
P(at least one vowel) = 1 – P(no vowels)

The probability of picking no vowel from the first set is 3/5.  The probability of picking no vowel from the second set is 5/6.  In order to get no vowels at all, we need no vowels from the first set AND no vowels from the second set.  According to the AND rule, we multiply those probabilities.

P(no vowels) = (3/5)*(5/6) = 1/2

P(at least one vowel) = 1 – P(no vowels) = 1 – 1/2 = [b]1/2[/b]

Answer = [b]C[/b]

 

[*]Suppose you flip a fair coin six times.  What is the probability of at least one head in six flips?

[*]5/8[/*]
[*]13/16[/*]
[*]15/16[/*]
[*]31/32[/*]
[*]63/64[/*]
[/list]
[/*]
[/list]

Show answer and explanation
P(at least one H) = 1 – P(no H’s)

In one flip, P(“not H”) = P(T) = 1/2.   We would need to have this happen six times—that is to say, six independent events joined by AND, which means they are multiplied together.

[url=https://magoosh.com/gmat/files/2012/12/tpatq_img2.png][img]https://magoosh.com/gmat/files/2012/12/tpatq_img2.png[/img][/url]Answer = [b]E[/b]

 

[*]In a certain game, you pick a card from a standard deck of 52 cards.  If the card is a heart, you win.  If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again.  The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won?   What is the probability that one will have at least two “heartless” draws on the first two draws, not picking the first heart until at least the third draw?

[*]1/2[/*]
[*]9/16[/*]
[*]11/16[/*]
[*]13/16[/*]
[*]15/16[/*]
[/list]
[/*]
[/list]

Show answer and explanation
A full deck of 52 cards contains 13 cards from each of the four suits.  The probability of drawing a heart from a full deck is 1/4.  Therefore, the probability of “not heart” is 3/4.

P(at least three draws to win) = 1 – P(win in two or fewer draws)

Furthermore,

P(win in two or fewer draws) = P(win in one draw OR win in two draws)

= P(win in one draw) + P(win in two draws)

Winning in one draw means: I select one card from a full deck, and it turns out to be a heart.  Above, we already said: the probability of this is 1/4.

P(win in one draw) = 1/4

Winning in two draws means: my first draw is “not heart”, P = 3/4, AND the second draw is a heart, P = 1/4.  Because we replace and re-shuffle, the draws are independent, so the AND means multiply.

P(win in two draws) =(3/4)*(1/4) = 3/16

P(win in two or fewer draws) = P(win in one draw) + P(win in two draws)

= 1/4 + 3/16 = 7/16

P(at least three draws to win) = 1 – P(win in two or fewer draws)

= 1 – 7/16 =[b] 9/16[/b]

Answer = [b]B[/b]

 

[b]Bonus Question[/b]

The probability is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least one of the tosses will turn up tails?

0.064

0.36

0.64

0.784

0.936

[url=https://gmat.magoosh.com/questions/839?utm_source=gmatblog&utm_medium=blog&utm_campaign=gmatquestions&utm_term=inline&utm_content=gmat-math-the-probability-at-least-question]Click here for the answer and video explanation![/url]

The next article in this series will explore [url=https://magoosh.com/gmat/gmat-probability-and-counting-techniques/]probability questions that involve counting techniques[/url].

The post [url=https://magoosh.com/gmat/gmat-math-the-probability-at-least-question/]GMAT Math: The Probability “At Least” Question[/url] appeared first on [url=https://magoosh.com/gmat]Magoosh Blog — GMAT® Exam[/url].
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FROM Magoosh Blog: GMAT Math: Calculating Combinations
This post was updated in 2024 for the new GMAT.

First, a few practice questions.  Remember — no calculator!

1) A radio station has to choose three days of the seven in a week to broadcast a certain program, and that set will repeat each week.  The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —-  nor does it matter whether the days the program airs are adjacent or not.  Absolutely any three of the seven weekdays can be chosen.   How many different three-day combinations of the seven weekdays can be constructed?

    (A) 9

    (B) 15

    (C) 21

    (D) 35

    (E) 56
2) Claudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.  Given these choices, how many candle + flower groupings can she select?

    (A) 54

    (B) 72

    (C) 96

    (D) 144

    (E) 432
3) A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families.  The template they have chosen has places for 3 large photos and 19 smaller photos.  The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots.  Given these choices, how many different possible albums could they create?

    (A) 3,150

    (B) 4,200

    (C) 5,040

    (D) 20,520

    (E) 84,000
In this post, we’ll discuss how to handle questions like this — without a calculator.

 

Combinations
Mathematically, a combination is a group of things, irrespective of order.  For example, {A, B, D} and {D, A, B} and {B, A, D} are all the same combination — order doesn’t matter at all. The expression nCr (read “n choose r”) is the expression for the number of combinations of r things, r choices, you can make from a pool of n unique items.  For example,

6C3 = the number of combinations of three one can choose from a pool of six unique items.

In a previous post about combinations, I give the following formula for nCr



where the exclamation point (“!”) is the factorial symbol — n! means the product of all the positive integers from n down to 1.  Using this formula, we could compute the value of 6C3



So, it turns out, there are twenty ways to pick a set of three items from a pool of six unique items.  That’s one way to calculate nCr, but it’s not the only way.

Pascal’s Triangle
The mathematician and philosopher Blaise Pascal (1623 – 1662) created a magical triangular array of numbers known now as Pascal’s Triangle:



How does this pattern work?  Well, of course, the edges are diagonals of 1’s.  Every inside number is the sum of the two numbers above it in the previous row, diagonally to the left and diagonally to the right.  For example, the 2 is the sum 1+1; both 3’s are the sum 1+2; both 4’s are the sums 1+3; the 6 is the sum 3+3, etc.  They often show Pascal’s Triangle to grade school students to give them practice with addition.

Despite its relatively easy origins, Pascal’s Triangle is a treasure trove of miraculous mathematical properties.  Most relevant for us right now is: Pascal’s Triangle is, among other things, an array of all possible nCr’s.

nCr = the rth entry of the nth row of Pascal’s Triangle

In that definition, we have to be careful — we have to start counting at zero instead of one.  The top 1 on Pascal’s Triangle is the zeroth row, zeroth entry, 0C0 = 1 (a relatively meaningless number in terms of combinations!)  The next row (1, 1) is the first row, and the next row is the second row (1, 2, 1), etc.  Notice that the second number in any row (as well as the penultimate number in any row) equals the row number. The first number (always 1) is actually the zeroth entry, so that second number would actually be the first entry — the first entry of the nth row always equals n.  In other words

nC1 = n

That makes sense: if we have n different items, we have exactly n ways of selecting any one item.  Those entries, the first entries of each row, line along a diagonal down the left side of the triangle.  Because of the complete symmetry of the triangle, this always equals the numbers on the corresponding diagonals on the right side, which would be the (n-1) entries of each row.  Thus:

nC1 = nC(n-1) = n

When you have to figure out nCr when n & r are both relatively small numbers, it may be easier simply to jot down the first few rows of Pascal’s Triangle.  For example, with what we have showing, we can see that 6C3, the 3rd entry of the 6th row, is 20 — the same as the answer we found via the factorials formula.

Things get even more interesting when we move to the next diagonal in, shown in green here:



These numbers, the set of the second entries in each row, are the triangular numbers.  Among other things, the second entry in the n row is the sum of the first n-1 positive integers.  For example

3 = 2 + 1

6 = 3 + 2 + 1

10 = 4 + 3 + 2 + 1  etc.

The formula for this is:



Because we have a formula, we can calculate this for much higher numbers.  For 21C2, we would have to write out everything to the twenty-first row of Pascal’s Triangle, an arduous undertaking.  Rather, we could simply use the formula



Notice that the symmetry of Pascal’s Triangle also provides tremendous insight into the nature of the nCr numbers.  First of all, in any row, the second entry, the triangular number in that row, must be equal to the third-to-last entry of the row, that is, the (n-2) entry of the row.  Thus



Thus, via the triangular numbers, we have a formula, not only for the second entry of each row, but also for the third-to-last entry of every row.  Thus, it’s very easy to figure out the first three or last three numbers in any row.  More generally, symmetry guarantees that:

nCr = nC(n-r)

If you think about combinations this makes sense: if we have a pool of n unique items, then every time we choose a unique set of r items, we necessarily exclude a corresponding unique set of (n-r) items.  In other words, there is necessarily a 1-to-1 correspondence between unique sets of r elements and unique sets of the other (n-r) elements —- because there’s a 1-to-1 correspondence, the number of each must always be the same.  This is precisely what that equation says.

 

Practice
That discussion was liberally peppered with hints about how to do the above three questions.  If you had trouble with them on the first pass, you may want to give them a second look before proceeding to the explanations below.  Here’s an additional question from inside Magoosh:

4) http://gmat.magoosh.com/questions/847

 

Practice question explanations
1) Behind the story, we are really being asked to evaluate 7C3.  We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row.  We see that 7C3, the third entry of the seventh row, is 35.  Answer = D.

2) For this one, we have to use the Fundamental Counting Principle (FCP) as well as information about combinations.  For the flowers, we want 9C8,  which by the symmetry of Pascal’s Triangle, has to equal 9C1, the first entry in the row, which of course equals the row number.

9C8 = 9C1 = 9

That’s the number of flower combinations.  For the candles, 4C2, we read the second entry of the fourth row of Pascal’s Triangle.

4C2 = 6

Now, by the FCP, we multiply these for the total number of centerpiece arrangements: 6*9 = 54.  Answer = A

3) For the large photos, we need 6C3, which we calculated in the article:

6C3 = 20

For the smaller photos, we need 21C19, which by symmetry must equal 21C2, and we have a formula for that.  In fact, in the article above, we already calculated that 21C2 = 210.

Now, by the FCP, we just multiply these: total number of possible albums = 20*210 = 4200.  Answer = B

 

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FROM Magoosh Blog: GMAT Quant: Roots
This post was updated in 2024 for the new GMAT.

Master these seemingly intimidating mathematical symbols!

Practice Questions
First, try these practice questions.

1) The numbers a, b, and c are all non-zero integers. Is a > 0?

Statement #1:

Statement #2:  

2) The numbers a, b, and c are all non-zero integers. Is a > 0?

Statement #1:

Statement #2:  

 

Square Roots
When you square a number, you are multiplying it by itself, e.g. 6*6 = 36.  When you take the square-root of a number, you are undoing the square, going backwards from the result of squaring to the input that was originally squared:
.  Similarly, 8*8 = 64, so
.  As long as all the numbers are positive, everything is straightforward.

It’s easy to find the square root of a perfect square.  All other square roots are ugly decimals.  For estimation purposes on the very hardest GMAT questions, it might be useful to memorize that
and
, but without a calculator, no one is going to ask you to calculate the values of any decimal square roots bigger than that.  If something like
shows up, all you have to recognize is between what integers you would find that decimal.  For example,



therefore



therefore



It’s also good to know how to simplify square roots.

The Symbol: Positive or Negative?


 

What is the name of this symbol?  The benighted unwashed masses will call this simply the “square root symbol”, but that’s not the full story.  The technical name is the “principal square root symbol.” Here, “principal” (in the sense of “main” or “most important”) means: take the positive root only.

This thickens the plot.  The equation
has two solutions, x = +4 and x = -4, because
and
, and the GMAT will impale you for only remembering one of those two.  At the same time,
has only one output:
only.  When you yourself undo a square by taking a square root, that’s a process that results in two possibilities, but when you see this symbol as such, printed as part of the problem, it means find the positive square root only.

Notice that we can take the square root of zero:
, so
, perfectly legal.  Notice, also, we cannot take the square root of a negative — for example,
— because that involves leaving the real number line.  There are branches of math that do this, but it’s well beyond the scope of the GMAT.

 

Cubes and Cube Roots
When we raise a number to the third power,
, that is called “cubing” it (because if we had a cube of side = 2, then the “cube” of that number would equal the volume of the cube).  Here,
.  A cube root simply undoes this process:
.  As with a square roots, it’s easy to find the cube roots of perfect cubes, and on the GMAT you would never be expected to find an ugly decimal cube root without a calculator.

Cubes and cube roots with negatives get interesting.  While
, it turns out that
.   When you multiply two negatives you get a positive, but when you multiply three negatives, you get a negative.  More generally, when you multiply any even number of negatives you get a positive, but when you multiply any odd number of negatives, you get a negative.  Therefore, when you cube a positive, you get a positive, but if you cube a negative, you get a negative.

This means: while you can’t take the square root of a negative, you certainly can take the cube root of a negative.  Undoing the equation
, we get
.  In general, the cube root of a positive will be positive, and the cube root of a negative will be negative.

It can also be a time-saver to remember the first five cubes:











You generally will not be expected to recognize cubes of larger numbers.  Knowing just these will translate handily into all sorts of related facts: for example,
and
.

If you remember just this, you will be well-prepare for whatever the GMAT asks you about roots.

 

Additional Practice Question
3) http://gmat.magoosh.com/questions/91

 

Explanations of the Practice Questions
1) All that is given in the prompt is that a, b, and c are non-zero integers.

Statement #1: the result of square anything is always positive, so whether b is negative or positive, a must be positive.  This statement, by itself, is sufficient.

Statement #2: since the square root symbol is printed as part of the problem, the output of the sqrt{c} must be positive.  We know for a fact that a must be positive.  Again, this statement, by itself, is sufficient.

Both statements are sufficient.  Answer = D.

2) Again, all that is given in the prompt is that a, b, and c are non-zero integers.

Statement #1: now, if we cube a positive, we get a positive, but if we cube a negative, we get a negative.  The numbers a & b are either both positive or both negative, but since we don’t know the sign of b, we cannot determine the sign of a.  This statement, by itself, is insufficient.

Statement #2: if we take the cube root of a positive, we will get a positive, but if we take the cube-root of a negative, we get a negative.  The numbers a & c are either both positive or both negative, but since we don’t know the sign of c, we cannot determine the sign of a.  This statement, by itself, is insufficient.

Combined Statements: If we put both statements together, we get that all three numbers, a, b, and c, have to have the same sign: either all three are positive, or all three are negative.  We have no further information that would allow us to determine which of those two is the case.  Thus, even with combined statements, we still do not have enough information to give a definitive answer to the prompt question.  Combined, the statements are still insufficient.  Answer = E

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FROM Magoosh Blog: GMAT Math: Terminating and Repeating Decimals
[img]https://magoosh.com/gmat/files/2020/03/terminating-and-repeating-decimals.png[/img]

[b]This post was updated in 2024 for the new GMAT.[/b]

You might not feel decimals are the most exciting thing in the world, but just look at our friend [b][img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_993.5_8edb2cf68079344a2edd739531259f6c.png[/img]
[/b], a decimal with its own [url=https://www.piday.org/]holiday[/url]! In this edition of GMAT Math, we’re going over two specific types of decimals: terminating and repeating decimals.  Learn about how to identify and solve questions with these decimals. Don’t forget to test your understanding with the practice questions at the end!

Rational Numbers
Integers are positive and negative whole numbers, including zero.  Here are the integers:

{ … -3, -2, -1, 0, 1, 2, 3, …}

When we take a ratio of two integers, we get a rational number.

[list]
[*]A rational number is any number of the form a/b, where a & b are integers, and b ≠ 0.[/*]
[*]Rational numbers are the set of all [url=https://magoosh.com/gmat/fractions-on-the-gmat/]fractions[/url] made with integer ingredients.   Notice that all integers are included in the set of rational numbers, because, for example, 3/1 = 3.[/*]
[/list]
 

Rational Numbers as Decimals
When we make a decimal out of a fraction, one of two things happens.  It either terminates (comes to an end) or repeats (goes on forever in a pattern).  Terminating rational numbers include:

1/2 = 0.5

1/8 = 0.125

3/20 = 0.15

9/160 = 0.05625

 

Repeating rational numbers include:

1/3 = 0.333333333333333333333333333333333333…

1/7 = 0.142857142857142857142857142857142857…

1/11 = 0.090909090909090909090909090909090909…

1/15 = 0.066666666666666666666666666666666666…

 

When Do Rational Numbers Terminate?
The GMAT won’t give you a complicated fraction like 9/160 and expect you to figure out what its decimal expression is.  BUT, the GMAT could give you a fraction like 9/160 and ask whether it terminates or not.  How do you know?

Well, first of all, [b]any terminating decimal (like 0.0376) is, essentially, a fraction with a power of ten in the dominator[/b]; for example, 0.0376 = 376/10000 = 47/1250.  Notice we simplified this fraction, by cancelling a factor of 8 in the numerator.  Ten has factors of 2 and 5, so any power of ten will have powers of 2 and powers of 5, and some might be canceled by factors in the numerator , but no other factors will be introduced into the denominator.  Thus, if the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, then it can be written as something over a power of ten, which means its decimal expression will terminate.

[list]
[*]If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates.  If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.[/*]
[/list]
Here’s some examples of this concept at work:

[list]
[*]1/24 repeats (there’s a factor of 3)[/*]
[*]1/25 terminates (just powers of 5)[/*]
[*]1/28 repeats (there’s a factor of 7)[/*]
[*]1/32 terminates (just powers of 2)[/*]
[*]1/40 terminates (just powers of 2 and 5)[/*]
[/list]
Notice, as long as the fraction is in lowest terms, the numerator doesn’t matter at all. Since 1/40 terminates, then 7/40, 13/40, or any other integer over 40 also terminates. Since 1/28 repeats, then 5/28 and 15/28 and 25/28 all repeat; notice, though that 7/28 doesn’t repeat, because of the cancellation: 7/28 = 1/4 = 0.25.

Shortcut Decimals to Know
There are certain decimals that are good to know as shortcuts, both for fraction-to-decimal conversions and for fraction-to-percent conversions.  These are:

[list]
[*]1/2 = 0.5[/*]
[*]1/3 = 0.33333333333333333333333333…[/*]
[*]2/3 = 0.66666666666666666666666666…[/*]
[*]1/4 = 0.25[/*]
[*]3/4 = 0.75[/*]
[*]1/5 = 0.2 (and times 2, 3, and 4 for other easy decimals)[/*]
[*]1/6 = 0.166666666666666666666666666….[/*]
[*]5/6 = 0.833333333333333333333333333…[/*]
[*]1/8 = 0.125[/*]
[*]1/9 = 0.111111111111111111111111111… (and times other digits for other easy decimals)[/*]
[*]1/11 = 0.09090909090909090909090909… (and times other digits for other easy decimals)[/*]
[/list]
Irrational Numbers
There’s another category of decimals that don’t terminate (they go on forever) and they have no repeating pattern.   These numbers, the non-terminating non-repeating decimals, are called the [b]irrational numbers[/b].

[list]
[*] It is impossible to write any irrational number as a ratio of two integers.[/*]

[/list]
Mr. Pythagoras (c. 570 – c. 495 bce) was the first to prove a number irrational: he proved that the square-root of [img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_990.5_1b3047e87641ecfdcdbfc48989c0da9a.png[/img]
is irrational.  We now know: all square-roots of integers that don’t come out evenly are irrational.  Another famous irrational number is [img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_993.5_8edb2cf68079344a2edd739531259f6c.png[/img]
, or pi, the ratio of a circle’s circumference to its diameter.  For example,

That’s the first 70 digits of pi, and the digits never repeat—they go on forever with no repeating pattern.  There are infinitely many irrational numbers: in fact, the infinity of irrational numbers is infinitely bigger than the infinity of the rational numbers, but that gets into some math that is much more advanced than what you need to know for the GMAT.

Terminating and Repeating Decimals: Practice Questions
Now here’s your chance to test your understanding! Try to answer these practice questions and then check the answer and explanation.

[list]
[*][img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_979_62e27c937c445d71f3f3e68df3578098.png[/img]

[*]2/27[/*]
[*]3/2 [/*]
[*]3/4[/*]
[*]3/8[/*]
[*]9/16[/*]
[/list]
[/*]
[/list]
 

Show answer and explanation
From our shortcuts, we know 0.166666666666… = 1/6, and 0.444444444444… = 4/9.  Therefore (1/6)*(9/4) = 3/8.

Answer = [b]D[/b]

 

And now for a sample question from our [url=https://gmat.magoosh.com?utm_source=gmatblog&utm_medium=blog&utm_campaign=gmatquestions&utm_term=inline&utm_content=gmat-math-terminating-and-repeating-decimals]GMAT product[/url]:

2. Given that [img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_993.5_163649480838189dca87be31c32bce7b.png[/img]
represents a decimal in which the digit k repeats without end, then what is the value of [img]https://magoosh.com/gmat/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_969_31e0bdd42f6fc6d56d0a7fc6a9ba5661.png[/img]
?

[/list]
0.1

1

4.5

6

18

[url=https://gmat.magoosh.com/questions/12628?utm_source=gmatblog&utm_medium=blog&utm_campaign=gmatquestions&utm_term=inline&utm_content=gmat-math-terminating-and-repeating-decimals]Click here for the answer and video explanation![/url]

If you’d like to practice more with decimals, check out our [url=https://magoosh.com/gmat/gmat-practice-questions-with-fractions-and-decimals/]GMAT practice questions with fractions and decimals[/url].

The post [url=https://magoosh.com/gmat/gmat-math-terminating-and-repeating-decimals/]GMAT Math: Terminating and Repeating Decimals[/url] appeared first on [url=https://magoosh.com/gmat]Magoosh Blog — GMAT® Exam[/url].
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FROM Magoosh Blog: Modifying a GMAT Study Schedule for Advanced Students


As an advanced GMAT exam taker, you’re already familiar with the basics of the test and have likely gone through numerous practice sessions. Now, it’s about fine-tuning your approach to ensure peak performance on test day. Here’s a comprehensive guide to help you optimize your study schedule by making the most of your preparation time.

Key GMAT Modifications for Advanced Students
  • Skip Basic Lessons: If you’re already comfortable with the basics, skip the introductory lessons on GMAT format, foundational test-taking strategies, and basic math and verbal concepts.
  • Focus on High-Difficulty Practice Questions: Spend time on the more challenging practice questions. In your Magoosh account, select the Hard and Very Hard practice questions. Of course, that’s only if you’ve mastered the concepts tested in the easy and medium categories.
  • Review Advanced Concepts: Concentrate on advanced topics by digging into the Lessons page on your Magoosh Dashboard. You’ll notice, depending on whether you’re using the three, two, or one month schedule, that not all lessons are included. The lessons that have been left out are the ones that cover the harder, less frequently tested content. Mastering strategies for those high-difficulty, low-frequency topics can significantly boost your score.
  • Utilize Official Guides and High-Quality Resources: While Magoosh offers a great variety of practice questions, its pool is limited. For advanced students looking to push their scores into the top percentiles, supplementing with GMAT Official Guide (OG) questions is crucial. The OG questions are written by the same people who create the GMAT, ensuring that you practice with the most accurate and representative questions. Use the OG question bank to create custom practice sessions and simulate test conditions as closely as possible.
  • Refine Test-Taking Strategies: Fine-tuning your strategies can lead to significant improvements in your performance. Consider the following:
  • Time Management: Develop a strict timing strategy for each section to ensure you complete all questions without rushing. Here are the averages you should aim for:
    • Reading Comprehension: A total of around 6 minutes for a shorter, three-question passage and a total of around 8 minutes for a longer, four-question passage.
    • Critical Reasoning: Around 2 minutes per question.
    • Quantitative Reasoning: Around 2 minutes per question.
    • Data Insights: Around 2.25 minutes per question.
  • Answer Elimination: Enhance your ability to quickly eliminate incorrect answer choices. Practice this with challenging questions to improve speed and accuracy.
  • Adaptive Strategy: Adapt your approach based on the difficulty level of the questions. For harder questions, ensure you don’t spend too much time, which could result in not completing the section.
Hardest GMAT Concepts by Section
Curious about the concepts and topics that are generally associated with the most challenging GMAT questions? We’ve listed them below for all three sections of the GMAT:

Quantitative Reasoning

  • Combinatorics and Probability: Permutations, combinations, and probability scenarios.
  • Advanced Algebra: Complex equations, inequalities, and functions.
  • Number Properties: Prime numbers, least common multiples, greatest common divisors, and advanced factorization.
  • Word Problems: Multi-step, layered word problems that require advanced analytical skills.
Verbal Reasoning

  • Critical Reasoning: Evaluating complex arguments, identifying assumptions, and strengthening or weakening arguments.
  • Reading Comprehension: Analyzing dense and sophisticated passages, understanding nuanced arguments, and answering inference questions.
Data Insights

  • Data Sufficiency: Evaluating statements methodically, particularly those that mix verbal reasoning with quantitative analysis.
  • Integrated Reasoning: Interpreting complex data from graphs, tables, and multi-source reasoning problems.
  • Advanced Calculations: Using logical and analytical skills to solve problems involving multiple variables and data sets.
Sample Modified GMAT Schedule for Advanced Students

As an example, here’s a week-by-week outline of how one could modify the three-month GMAT study plan:

Week 1-2: Diagnostic and Advanced Concept Review
  • Day 1: Take a full-length diagnostic test. Review results and identify weak areas.
  • Day 2-3: Look through the week’s lessons and quizzes and determine the ones to which you will devote your time and attention.
  • Day 4-6: Focus on advanced topics in Quantitative Reasoning (e.g., number properties, advanced algebra) and Critical Reasoning (e.g., argument evaluation and assumption questions).
Week 3-4: Intensive Practice and Error Analysis
  • Day 1-3: Look through the week’s lessons and quizzes to determine the ones to which you will devote your time and attention. Check the dashboard for supplemental lessons not included in your chosen study schedule.
  • Day 2-3: Practice high-difficulty questions from the OG and Manhattan Prep question banks.
  • Day 4-5: Review mistakes and re-attempt incorrect questions. Update your error log.
  • Day 6: Take a timed, mixed practice test (Quantitative, Verbal, Data Insights).
Week 5-6: Full-Length Practice Tests and Strategy Refinement
  • Day 1: Take a full-length practice test under timed conditions. Analyze results.
  • Day 2-3: Focus on timing strategies, pacing, and question prioritization.
  • Day 4-5: Look through the week’s lessons and quizzes to determine the ones to which you will devote your time and attention. Check the dashboard for supplemental lessons not included in your chosen study schedule.
  • Day 6: Review complex problem types (e.g., combinatorics, probability, inference questions).
Week 7-8: Focus on Weak Areas and Advanced Drills
  • Day 1-2: Intensive practice on weak areas identified from previous tests.
  • Day 3-4: Look through the week’s lessons and quizzes to determine the ones to which you will devote your time and attention. Check the dashboard for supplemental lessons not included in your chosen study schedule.
  • Day 5: Drills on high-frequency and high-difficulty question types.
  • Day 6: Mixed practice sessions focusing on speed and accuracy.
Week 9-10: Strategy Sessions and Final Reviews
  • Day 1: Take another full-length practice test. Focus on test-taking stamina.
  • Day 2-3: Review advanced test-taking strategies, such as eliminating wrong answers and educated guessing.
  • Day 4-5: Look through the week’s lessons and quizzes to determine the ones to which you will devote your time and attention. Check the dashboard for supplemental lessons not included in your chosen study schedule.
  • Day 6: Rest and light review of, error log, flashcards or notes.
Week 11-12: Simulation and Final Prep
  • Day 1: Full-length practice test. Mimic test day conditions.
  • Day 2-5: Analyze performance, focus on last-minute weak spots.
  • Day 6: Final review of key concepts and test strategies.
Conclusion

Advanced GMAT students should focus on refining their skills and mastering high-difficulty questions. By modifying a Magoosh study schedule and concentrating on advanced practice and strategic review, you can significantly improve your chances of achieving a top score.

Good luck with your preparation!

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FROM Magoosh Blog: How to Get a Top Score on the New GMAT


Aiming for a top score on the GMAT is a goal shared by many aspiring MBA applicants. With the introduction of the updated GMAT back in November 2023, understanding how close your current score is to your ultimate goal and just how to achieve a score that places you in the highest percentiles requires a fresh approach. This guide will walk you through the essentials, from understanding the new scoring system to strategic study tips that will help you achieve an impressive GMAT score.

Understand How the Test is Scored

The new GMAT has redefined what constitutes a top score. Previously, a score of 700+ was considered the gold standard, placing test-takers in the upper echelon. Now, the scoring system has been revamped, and it’s crucial to grasp these changes to set realistic goals.

New GMAT Scoring:

  • Overall Score Composition: The total score ranges from 205 to 805, incorporating three main sections: Quantitative Reasoning, Verbal Reasoning, and Data Insights. Each section contributes equally to your overall score. Thus, it is essential to perform well on all three sections if you’re trying to achieve a top score.
  • Percentile Rankings: Percentiles are what MBA programs use to evaluate an applicant’s GMAT performance. Therefore, understanding percentile rankings is critical for setting your target score and developing an effective study plan. For example, if you set your sights on a top-tier programs, you should aim for a score in at least the 90th percentile, which corresponds to a GMAT score of 645. For a more in depth look at GMAT percentiles, check out our post on Score Charts and Percentile Rankings.
Know Your Baseline Score [/b]

One of the most important steps in your GMAT prep is to know your starting point–a.k.a your baseline score. If you hope to land in one of the highest GMAT percentiles, you need to know the gap between your starting score and your dream score. Take a full-length practice test as soon as possible to determine the progress you need to make.

Know Where to Focus[/b]

Achieving a high score requires a strategic approach. Check out the top tips from a Magoosh student who scored in the 99th percentile!



Now, let’s take a high-level look at where and how to focus your efforts in each part of the exam to achieve a top GMAT score.

Quantitative Reasoning

Key Topics: Algebra, Coordinate Geometry, Arithmetic, and Word Problems.

Hardest Question Types:

  • Advanced Algebra: Topics such as quadratic equations, functions, and inequalities can be challenging, particularly when they are part of word problems that require setting up and solving complex equations.
  • Coordinate Geometry: Problems involving properties and equations of lines and curves in the coordinate plane can be difficult, especially when they require multi-step reasoning and integration of various algebraic concepts.
  • Complex Word Problems: These problems often require multiple steps and the integration of various mathematical concepts, making them time-consuming and prone to errors.

Strategy: Master fundamental concepts and practice with advanced problem sets to increase speed and accuracy. Focus on breaking down complex problems into manageable steps and become adept at quickly identifying the most efficient solution path.

Verbal Reasoning

Key Topics: Reading Comprehension and Critical Reasoning.

Hardest Question Types:

  • Reading Comprehension: Long passages with dense, complex information. These questions often require not just understanding the content but also making inferences and understanding the author’s tone and purpose.
  • Critical Reasoning: These questions test your ability to evaluate arguments and reasoning. The hardest ones often involve abstract concepts or multi-part logical structures that require a deep understanding of the argument’s components.
  • Inference Questions: These questions, in both Reading Comprehension and Critical Reasoning, require you to draw logical conclusions based on information provided in the passage, which can be tricky when the passage is abstract or densely written.

Strategy: Improve your reading speed and comprehension by regularly reading complex materials. Focus on identifying argument structures and common logical fallacies. Practice breaking down passages and questions to their core components and systematically eliminating incorrect answer choices.

Data Insights

Key Topics: Data Interpretation, Multi-Source Reasoning, Graphics Interpretation, and Data Sufficiency.

Hardest Question Types:

  • Multi-Source Reasoning: These questions present information in various formats (tables, graphs, text) and require synthesizing data from multiple sources to answer complex questions.
  • Graphics Interpretation: Interpreting and analyzing data from charts, graphs, and other visual data presentations can be challenging, especially when the questions involve multi-step calculations or require drawing inferences from incomplete data.
  • Quantitative and Verbal Data Sufficiency: These questions call upon both quantitative and verbal skills, requiring a unique approach to determine the sufficiency of given information.

Strategy: Get comfortable with different data formats and practice synthesizing information quickly. Familiarize yourself with interpreting complex data sets and practice using logical and analytical skills to draw conclusions. Use a systematic approach to determine the sufficiency of information and become proficient in handling multi-step problems efficiently.

Never Make a Mistake More Than Once

The path to a high GMAT score is paved with learning from your errors. Here’s how to ensure you don’t repeat mistakes:

  • Error Log: Maintain a detailed log of every mistake you make during practice. Include the type of error, the reason behind it, and the correct approach. Check out Magoosh’s free Error Log Template.
  • Review Regularly: Periodically review your error log to identify patterns. This will help you pinpoint areas that need more focus.
  • Targeted Practice: Once you identify common mistakes, engage in targeted practice to strengthen those weak areas. This focused approach will help you eliminate recurring errors.
Study Consistently

Consistency is key to mastering the GMAT. Here are some tips to help you maintain a steady study routine:

  • Daily Practice: Allocate time each day for GMAT preparation. Even if it’s just an hour, daily practice helps reinforce learning and build momentum.
  • Balanced Study Plan: There is a lot of ground to cover in preparing for the GMAT. If you haven’t done so already, you’ll want to organize your efforts into a realistic study schedule like the ones available through Magoosh. Ensure your study plan covers all sections of the test. Avoid over-focusing on one area at the expense of others, and if you’re striving for an elite score, you’ll need to consider building a schedule curted for more advanced students.
  • Use Quality Resources: Invest in reputable GMAT prep materials, like those found in GMAC’s Official Guide, Magoosh, or Manhattan. If you find that you need additional structure and support, consider investing in a prep course. Check out Magoosh’s Free One-Week GMAT Prep Course Trial.
  • Take Practice Tests: Regularly take full-length practice tests under timed conditions. This not only builds stamina but also helps you get accustomed to the test’s format and timing.
Final Thoughts

Scoring in the 90th (or above) percentile on the new GMAT requires a deep understanding of the test’s format, strategic focus on key areas, diligent error management, and consistent study habits. By following the guidelines outlined in this post, you’ll be well on your way to achieving a top score and opening the doors to the business school of your dreams.

Happy studying, and best of luck on your GMAT journey!

The post How to Get a Top Score on the New GMAT appeared first on Magoosh Blog — GMAT® Exam.
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FROM Magoosh Blog: Average GMAT Scores: Top 50 MBA Programs


Wondering what the relationship between GMAT scores and the top MBA programs in America are? We’re here to show you what the average GMAT scores are for the entire test taking pool, along with scores for the top 50 U.S. based programs. You can use this blog to help set your score goals and smartly jumpstart your GMAT prep.

Table of Contents
average total GMAT score for the new, shorter exam is 546.01[/b].

We can also break the mean scores down by section:

Section
Mean Score

Verbal
78.99

Quantitative
77.71

Data Insights
74.41

Total Score
546.01

Sample Size: 866,640

Data Period: 2017-2022

top business school[/b]. At the top 20 business schools in America, you generally need a score of at least 665 to be competitive. Still, even in these top programs, some applicants are accepted with scores lower than 645. And a school’s own stated GMAT score preferences can change from year to year. At schools ranked from 30-50 scores tend to range from the high 500s to the low 600s, albeit with outliers on both sides.

USNWR Ranking
School

Average New GMAT Score
Average GMAT Classic Score
GMAT Classic Middle 80% or Accepted Student Range

1
Stanford GSB
685
738
Range: 630-790

1
UPenn (Wharton)
685
728
Does not disclose

3
Northwestern (Kellogg)
685
731
Range: 620-780

3
University of Chicago (Booth)
685
728
Range: 600-780

5
MIT (Sloan)
685
730
Middle 80%: 700-760

6
Harvard
685
740
Range: 500-790

7
NYU (Stern)
685
732
Middle 80%: 700-760

7
UC Berkeley (Haas)
685
733
Middle 80%: 680-770

7
Yale
675
720
Middle 80%: 680-760

10
Dartmouth (Tuck)
675
726
Range: 630-800

10
University of Virginia (Darden)
665
716
Middle 80%: 680-750

12
Columbia University
685
730
Middle 80%: 700-760

12
Duke (Fuqua)
665
715
Middle 80%: 670-760

12
University of Michigan – Ann Arbor (Ross)
675
719
Middle 80%: 670-760

15
Cornell (Johnson)
665
710
Middle 80%: 660-750

16
Carnegie Mellon (Tepper)
655
705
Middle 80%: 650-750

16
UT-Texas – Austin (McCombs)
655
704
Middle 80%: 670-740

18
Emory (Goizueta)
665
709
Middle 80%: 640-740

18
University of Southern California (Marshall)
675
722
Middle 80%: 681-760

20
Indiana University (Kelley)
635
685
Does not disclose

20
UCLA (Anderson)
665
709
Middle 80%: 640-760

20
UNC (Kenan-Flager)
655
696
Does not disclose

20
Vanderbilt (Owen)
645
687
Middle 80%: 640-730

24
Georgetown (McDonough)
655
695
Middle 80%: 630-743

25
Georgia Institute of Technology (Scheller)
645
694
Middle 80%: 640-722

26
Washington University (Olin)
655
696
Does not disclose

27
University of Georgia (Terry)
615
668
Middle 80%: 610-710

27
University of Washington (Foster)
665
710
Middle 80%: 660-740

29
Rice University (Jones)
655
702
Middle 80%: 680-730

30
Ohio State University (Fisher)
655
698
Middle 80%: 640-740

30
University of Notre Dame (Mendoza)
665
710
Does not disclose

32
Arizona State (W.P. Carey)
655
702
Does not disclose

32
University of Rochester (Simon)
Does not disclose
Does not disclose
Middle 80%: 600-700

34
Southern Methodist University (Cox)
645
694
Middle 80%: 650-730

35
University of Minnesota (Carlson)
635
680
Does not disclose

36
University of Florida (Warrington)
615
650
Does not disclose

37
BYU (Marriott)
615
668
Does not disclose

38
University of Texas at Dallas (Jindal)
645
689
Middle 80%: 650-700

38
University of Utah (Eccles)
595
639
Does not disclose

40
William and Mary (Mason)
585
620
Does not disclose

41
Michigan State (Broad)
615
665
Middle 80%: 600-720

41
University of Maryland (Smith)
615
656
Does not disclose

43
University of Wisconsin
615
651
Middle 80%: 590-710

44
TCU (Neely)
575
612
Does not disclose

44
UC Irvine (Merage)
635
675
Does not disclose

46
Boston College (Carroll)
595
643
Middle 80%: 581-680

47
Texas A&M (Mays)
615
649
Does not disclose

47
University of Tennessee (Haslam)
615
673
Does not disclose

50
Boston University (Questrom)
635
680
Middle 80%: 640-720

50
Iowa State (Ivy)
555
577
Does not disclose

50
University of Arizona (Eller)
635
684
Does not disclose

GMAC, the folks who create the GMAT, the GMAT score percentiles reveal the link between GMAT score and percentile rank of everyone who takes the GMAT. Percentile rankings help you see how your test performance fares against all other test takers in a certain window. Schools will sometimes publish percentiles, rather than scores, as their benchmarks for acceptance. Looking at percentiles as well as section and overall score can help you set smarter goals.

Score
Mean Score
Percentile Ranking

805

100%

755

100%

705

99%

655

93%

605

75%

555
546.01
53%

505

31%

455

17%

405

8%

355

3%

305

1%

255

0%

205

0%

GMAT percentiles work. If you’re not sure about your score, check out Magoosh’s GMAT score calculator first, then check out what this means for percentiles! Consider a Magoosh Premium Plan to help you meet your score goals to get into a top MBA program.

The post Average GMAT Scores: Top 50 MBA Programs appeared first on Magoosh Blog — GMAT® Exam.
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