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A Tricky Question on Negative Remainders [#permalink]
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FROM Veritas Prep Blog: A Tricky Question on Negative Remainders

Today, we will discuss the question we left you with last week. It involves a lot of different concepts – remainder on division by 5, cyclicity and negative remainders. Since we did not get any replies with the solution, we are assuming that it turned out to be a little hard.

It actually is a little harder than your standard GMAT questions but the point is that it can be easily solved using all concepts relevant to GMAT. Hence it certainly makes sense to understand how to solve it.

 

Question: What is the remainder when 3^(7^11) is divided by 5? (here, 3 is raised to the power (7^11))

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

Solution: As we said last week, this question can easily be solved using cyclicity and negative remainders. What is the remainder when a number is divided by 5? Say, what is the remainder when 2387646 is divided by 5? Are you going to do this division to find the remainder? No! Note that every number ending in 5 or 0 is divisible by 5.

2387646 = 2387645 + 1

i.e. the given number is 1 more than a multiple of 5. Obviously then, when the number is divided by 5, the remainder will be 1. Hence the last digit of a number decides what the remainder is when the number is divided by 5.

On the same lines,

What is the remainder when 36793 is divided by 5? It is 3 (since it is 3 more than 36790 – a multiple of 5).

What is the remainder when 46^8 is divided by 5? It is 1. Why? Because 46 to any power will always end with 6 so it will always be 1 more than a multiple of 5.

On the same lines, if we can find the last digit of 3^(7^11), we will be able to find the remainder when it is divided by 5.

Recall from the discussion in your books, 3 has a cyclicity of 4 i.e. the last digit of 3 to any power takes one of 4 values in succession.

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

and so on… The last digits of powers of 3 are 3, 9, 7, 1, 3, 9, 7, 1 … Every time the power is a multiple of 4, the last digit is 1. If it is 1 more than a multiple of 4, the last digit is 3. If it is 2 more than a multiple of 4, the last digit is 9 and if it 3 more than a multiple of 4, the last digit is 7.

What about the power here 7^(11)? Is it a multiple of 4, 1 more than a multiple of 4, 2 more than a multiple of 4 or 3 more than a multiple of 4? We need to find the remainder when 7^(11) is divided by 4 to know that.

Do you remember the binomial theorem concept we discussed many weeks back? If no, check it out here.

7^(11) = (8 – 1)^(11)

When this is divided by 4, the remainder will be the last term of this expansion which will be (-1)^11. A remainder of -1 means a positive remainder of 3 (if you are not sure why this is so, check last week’s post here). Mind you, you are not to mark the answer as (D) here and move on! The solution is not complete yet. 3 is just the remainder when 7^(11) is divided by 4.

So 7^(11) is 3 more than a multiple of 4.

Review what we just discussed above: If the power of 3 is 3 more than a multiple of 4, the last digit of 3^(power) will be 7.

So the last digit of 3^(7^11) is 7.

If the last digit of a number is 7, when it is divided by 5, the remainder will be 2. Now we got the answer!

Answer (C)

Interesting question, isn’t it?

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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3 Ways to Use Your SAT Study Habits in College [#permalink]
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FROM Veritas Prep Blog: 3 Ways to Use Your SAT Study Habits in College

By the time you’ve taken your last SAT, you may be ready to defenestrate the nearest standardized test. I’m here to advise you to resist throwing either an SAT test or the habits you picked up while studying under Veritas Prep – such as learning new vocabulary – out the window. In all seriousness, you really have learned valuable habits through the Veritas Prep SAT course that I personally regret not employing during my freshman year of college.

Freshman year of college was an especially rough year for me. My sleep cycle was off-balance, I was constantly cramming at the last minute, and I was consistent only in being late to class. While it’s possible to get through high school with a completely dysfunctional schedule, in college, it will not only sink your grades, but it will interfere with your social life and generally lead you into an unnecessary but extremely detrimental state of anxiety. I bounced back during my sophomore year, but I can’t help wishing that I’d known the following the strategies before I set foot on campus.

1. Keep Track

Veritas Prep gave you prepared notebooks to keep track of your scores, difficult problems, difficult vocabulary, and important practice problems. Make your own version for your toughest college classes so that you can quickly become aware of your performance (are your homework and test scores decreasing or increasing?) and identify how to solve tricky problems.

I can’t tell you how many times, my freshman year, I never really set about understanding a problem that had been confusing me all semester, and lost major points on test day as a result. It seems slightly absurd in retrospect, but in college, you won’t have the same supervision from parents or teachers that you did in high school. In college, a professor teaching a class of 200 students won’t say a word to you if you consistently miss a particular problem on your homework. It’s up to you to keep track.

2. Be a Critical Reader

In college, you are going to have to read an insane amount of material. One way to make sure that you actually understand what you are reading is to use the SAT Reading Strategies you’ve learned from Veritas Prep to your advantage. By the time you’ve finished the introduction, try to write down the main idea of the article. As you read, make occasional summaries, and pay attention to the particular claims the author makes.

You’ll rarely see a set of questions at the end of the article the way you often do in high school. While this may be a relief for some, it also means that you are responsible for making sure you understand what the article is about. Just because you aren’t instantly quizzed on it, doesn’t mean you won’t have to answer questions on it during finals.  It doesn’t hurt to look up words you don’t know – and add them to a list of vocabulary words – either.

3. Incorporate Your SAT Vocabulary into Your College Life

Regardless of how bored you felt while learning new vocabulary words, try to realize that you’ve been given an invaluable gift. Being able to describe your ideas with more precision is one of the greatest advantages of having a large vocabulary. You’ll not only impress your college professors with your papers, but you’ll be able to communicate with them more accurately and deeply than your classmates who cannot describe the world with the same precision as you. Finally, regardless of your ambitions, realize that the usage and meaning of a word are inseparable; if you don’t use the words in your real life, you will surely forget their meaning.

Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Here’s another article by Rita on scoring a perfect 2400.

By Rita Pearson
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School Profile: The Path of Enrichment at Williams College [#permalink]
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FROM Veritas Prep Blog: School Profile: The Path of Enrichment at Williams College

Williams College is on a quaint campus in Williamstown, Massachusetts and is ranked #16 on the Veritas Prep Elite College list. This liberal arts college has just under 2,200 students enrolled, primarily. With a focus on humanities and smaller class sizes, this is an ideal school for students looking for a more intimate and personalized education. The mission of Williams College is to not only help their students succeed, but to help them thrive; many services and programs throughout the campus achieve just that.

The faculty and staff at Williams College want their students to be well-rounded and exceptional additions to the world after completing their studies. This is done through their comprehensive academic curriculum and extensive educational assistance programs. Every student has a major but instead of minors they offer concentrations. These are compilations of specific topics pulled from an assortment of disciplines and departments.

There are no required courses at Williams; however, each student must take three humanities, social sciences, and science and math classes, two intensive writing courses, and one class on reasoning both mathematically and abstractly. The same goes with languages; they are not required courses, but students must enroll in at least one diversity study course. Grad-style research opportunities, overseas learning options, and specialty programs are offered at Williams to create highly developed students.

The campus life at Williams College is unique and designed to bring students, staff, and faculty together as a tight-knit community. Campus housing is split into four neighborhoods, Currier, Dodd, Spencer, and Wood; within each neighborhood are five to six different residences. There are three dining halls, two snack bars, a grab and go lunch program, and vending and catering operations on campus.

Among the luxuries that the campus provides are programs to enlighten students in self-discovery. The programs were developed to give students an understanding of and appreciation for their individuality. The Career Center is another place for students to hone in on their goals for the future with an exceptionally designed three step process. Campus life at Williams is all about enrichment, making sure each student is confident and comfortable in all aspects of life.

Williams College is an NCAA Division III school and part of the New England Small College Athletic Conference. There are 32 men’s and women’s varsity teams as well as junior varsity, club, and intramural teams. This campus also has physical education classes and fitness classes that have access to their state of the art facilities. Williams College is devoted to the health and fitness of their students; they require all students to earn four physical education credits as well as pass a swim test. More than 60 percent of the campus population participates in one of the athletic options, including faculty.

Ephraim Williams founded this college in 1793. Originally a men’s college, more than half of the student population is now female. Diversity and forward thinking are the foundations of this school filled with unique traditions. Students, faculty, family, and friends can all participate in eight hour trivia nights after every semester. The event is hosted by the college radio station, and all are put to the test with a crazy mixture of trivia while simultaneously performing tasks and identifying songs. This tradition has been around since 1966 entertaining the masses after grueling semesters. An even cooler event is Mountain Day, the annual canceling of classes on a random Friday in October by the President of the college, where students enjoy donuts, hot cider, and the sounds of a cappella groups. This college caters to students who want a well rounded college experience.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of ChicagoPomona College, and Amherst College, and more to see if those schools are a good fit for you.

By Colleen Hill
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GMAT at the Movies: What Austin Powers Can Teach You about S [#permalink]
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FROM Veritas Prep Blog: GMAT at the Movies: What Austin Powers Can Teach You about Similar Trianges

In this series we return to classic movies to learn fundamental strategies for GMAT Success.

In the Austin Powers movies the character known as “Dr. Evil” creates an exact version of himself, only smaller, that he calls “Mini-me.” The two characters have identical proportions even though one evil villain is 8 times the size of the other. The hero, Austin Powers, quickly recognizes the similarity, despite the difference in size. This is something that you will need to be able to do on the GMAT!

If you are not familiar with “Dr. Evil” and “Mini-me, watch the following clip:



This is what similar triangles are all about! Not the evil villain stuff, but the “same proportions, different size.” When you have proven that you have similar triangles you know that any ratio of a side of one triangle to the corresponding side of the other triangle will hold true for each of the sides and even for the height of those triangles.

As you can see from the diagram below all three angles are equal. The ratio of the lengths of the triangle will remain constant. So if A:a = 2:1 then B:b and C:c and even H:h will stay at that same ratio of 2:1



Recognizing Similar Triangles

Often the biggest difficulty that people have with these similar triangle problems is simply recognizing that they are, in fact, “similar.”

Most similar triangles on the GMAT are not like the diagram above. They are actually overlapping triangles that have one angle in common. Be on the lookout for that “shared angle.” That is usually the first clue that you have similar triangles!

In addition to the shared angle look for one of these other two clues that similar triangles are present:

1)      Parallel lines: If the triangle has a shared angle AND parallel lines then you have a similar triangle. For the diagram below you would be told that DE is parallel to AC. This creates similar triangles BDE and ABC.



2)      Right angles: If the triangles each have a right angle AND a shared angle then you have a similar triangle. In the diagram below you see that angle “D” is shared and that angles DCE and ABC are right angles. This means that you have similar triangles ABD and CDE.



Don’t wait for the GMAT to make similar triangles as obvious as Dr. Evil and Mini-Me. Watch out for shared angles, parallel lines, and right angles. And remember that easily recognizing similar triangles is “groovy baby, yeah!”

If you plan on taking the GMAT soon, we have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

 David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.
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How Hard is the Verbal Section of the GMAT? [#permalink]
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FROM Veritas Prep Blog: How Hard is the Verbal Section of the GMAT?

Two weeks ago I wrote an article about whether the GMAT was hard. It is a question I get asked regularly from many different students with many different interpretations of what “hard” actually means. On test day, you may get a question that seems impossible to solve, and yet most other students get it right. This means that the question wouldn’t be considered difficult by the GMAT (say a 500 level question), but for you it seemed exceptionally difficult. The notion of difficulty is thus subjective, and while many would argue that the GMAT is hard, I have a much simpler explanation I have been postulating for the past couple of years:

The GMAT is not hard, the GMAT is tricky.

Last time, I examined how the GMAT attempts to trick students by using subtle word meaning and blatant misdirection from a predominantly mathematical point of view. Today, I’d like to elaborate on how these same elements apply to the verbal section as well.

A brief recap for those who haven’t read the previous article: The difference between hard and tricky is primarily that the GMAT will not test any material that wasn’t covered in a standard high school curriculum. Obviously, having a degree in English literature will give you an edge on many types of verbal questions, but a post-secondary education in the language is not necessary to solve any problem. The reason for this is to put students on as even a footing as possible. The downside of this is that the material cannot be advanced, by its very nature its high school level material.

The GMAT therefore has to offer difficult questions based on material that’s not inherently too difficult. What are some easy ways to make simple material more challenging? The first one is the timing aspect, so you only have a limited amount of time to answer the questions, but moreover you feel the pressure of time running out on you constantly. If you had unlimited time to answer the questions, most people would score significantly higher on the GMAT, so managing your time is paramount to getting a top score.

This is the same reason as to why there’s no spell check on the AWA. With a spell check, it’s a lot harder to differentiate between someone who has a mastery of the English language and someone who can just rely on the red underline in Word (or my bane: the green underline). It also forces you to have to come up with synonyms or alternatives if you’re unsure of the ideal phrasing (or trying to paraphrase the word “question” again).

To highlight these elements, let’s look at simple question that underscores the trickiness of the GMAT:

Even today, lions can be seen ruling the African plains, hunting almost any animal that crosses its path and intimidating all but the most intrepid hunters.

(A) lions can be seen ruling the African plains

(B) lions are able to be seen ruling the African plains

(C) lions rule the African plains

(D) the lion rules the African plains

(E) the lion species rules the African plains

This sentence correction question asks us to choose among several answers that all sound pretty similar. In fact, the first three answer choices are very similar, just with varying degrees of superfluous text added to each. The other two answers also seem very similar, but play around with the number of the subject. There seems to be a split along the number of the subject, but other than that, the choices seem distressingly similar.

At first glance, many students concentrate on the first part of the sentence and essentially ignore everything after the underlined portion. After all, if it were important, wouldn’t it be underlined? This tends to lead to a differentiation among the first three answer choices, all of which essentially say the same thing. In this case, most students would gravitate towards answer choice C as it is the most succinct version of the text. However the slight meaning difference between answers A and C leads many students to debate the merits of each answer choice. Often this can lead to indecision between the choices and an educated guess just to move on to the next question.

However, if you’ve gone down this path here (or on another similar question), you’ve fallen into a classic GMAT trap. You’ve just spent time deciding between two answer choices that are both incorrect! This process can be very frustrating on practice tests, but you’ll never know whether this situation arose on the actual GMAT because you’ll never know what the correct answer was (the NSA would know, though). What happened in this situation? The GMAT misled you into contrasting two answer choices with virtually identical meanings.

The difference between the first three answer choices and the last two hinges on the number of the subject. If the subject is plural, we need lions; if it’s singular, we need lion or lion species (this is singular even though it doesn’t sound like it!). The key to making this decision lies in the pronoun “its” located at the end of the line. Since the pronoun is singular, the subject must also be singular in order to avoid making an antecedent agreement error. Neither answer choice A nor C can be correct, so it must be either D or E. The correct answer will be D as it is the only one that has a logical meaning. If the subject were the lion species, it would be nonsensical to imagine crossing paths with a species. Answer D is also more succinct, which adds to its appeal (like driving a nice car).

The decisions asked of you on the GMAT do not tend to be hard, but they also do not tend to be straight forward. A lot of questions will try to mislead you or trick you into focusing on the wrong thing. Spending a minute choosing between two incorrect answer choices seems absurd, and yet it happens time and time again on this exam. The rules of grammar being tested on this exam, much like the mathematical rules being tested in the quant section, are not the hardest rules imaginable. However, they are specifically chosen to tricky and deceptive.

Going back to the industrial strength lock analogy I used two weeks ago, the same lessons can be applied in both verbal and quant. If you know the combination to the safe, you will get the correct answer quickly. If you’re attempting a brute force approach with every possible combination, you will certainly run out of time. However if you know which options to eliminate and which options to keep, you’ll do well on the test. As Kenny Rogers put it: You got to know when to hold ‘em and know when to fold ‘em.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
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GMAT Tip of the Week: The Whole Sentence Mathers [#permalink]
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FROM Veritas Prep Blog: GMAT Tip of the Week: The Whole Sentence Mathers

Welcome back to Hip Hop Month in the Tip of the Week space, where today we’ll cover Sentence Correction’s most devious wordplay with the rap god of wordplay himself, Eminem. Fans of Slim Shady and connoisseurs of Sentence Correction alike will note the similarity between the two: sometimes, when you least expect it, a word all the way at the end will tie back so beautifully to one all the way at the beginning that it’s just mindblowing. In Eminem’s case, you have to rewind the track to listen to it again – did he really carry that rhyme all the way back like that?! – but on the GMAT you can’t rewind, so it’s important to heed Marshall’s advice well before you put on those noise-reduction headphones (Beats by Dre?) at the test center and zone into the verbal section:

The Whole Sentence Matters

One of Eminem’s most famous lyrics goes like this:

“I don’t give an **** if it’s dark or not

I’m harder than me trying to park a Dodge

When I’m drunk as f**k

Right next to a humungous truck

In a two car garage.”

As you’ll see this “inside out” rhyme scheme has evolved over time, but what he does here after “Dodge” is get onto another rhyme scheme (luck, truck, buck…) and then “surprise” the listener by coming back to Dodge/Garage when your mind has already gotten onto another scheme. 12 years later, this technique has become even more pronounced in his newer track “Headlights” (a surprising tribute to his mom):

Cause, one thing I never asked was where the **** my deadbeat dad was

F*** it, I guess he had trouble keeping up with every address

But I’d have flipped every mattress, every rock and desert cactus

Own a collection of maps and followed my kids to the edge of the atlas

If someone ever moved ‘em from me, that you could’ve bet your asses

If I had to come down the chimney dressed as Santa, kidnap ‘em

And although one has only met their grandma, once you pulled up

In our drive one night, as we were leaving to get some hamburgers

Me, her and Nate, we introduced you, hugged you

And as you left I had this overwhelming sadness

Come over me as we pulled off to go our separate paths, and

I saw your headlights as I looked back and

I’m mad I didn’t get the chance to thank you for being my mom and my dad

So mom, please accept this as a tribute I wrote this on the jet, I guess

I had to get this off my chest, I hope I get the chance to lay it ‘fore I’m dead

The stewardess said to fasten my seatbelt, I guess we’re crashing

By the time the listener gets to the end of this segment, you’ve almost completely forgotten about the bolded words above, but when Eminem hits that last word “crashing” that same rhyme scheme comes back for one last hurrah. Why is this important for the GMAT? Because this same art of “I bet you’ve forgotten the relationship between these words by now so I’m going to drop it in here and totally surprise you” is one of the techniques that testmakers use frequently to create difficult Sentence Correction:

Consider this question as an example:

Discovered by Dr. Dre as a teenage rap battle phenom, Eminem released ten Billboard number one singles and collected thirteen Grammys – plus an Academy Award for his single “Lose Yourself” from his autobiograhical film 8 Mile, in which he starred as rapper B. Rabbit – and countless other awards since he signed with Dre’s Aftermath Records.

(A) Discovered by Dr. Dre as a teenage rap battle phenom, Eminem released ten Billboard number one singles and collected thirteen Grammys

(B) Having been discovered by Dr. Dre as a teenage rap battle phenom, Eminem released ten Billboard number one singles and collected thirteen Grammys

(C) Discovered by Dr. Dre as a teenage rap battle phenom, Eminem has released ten Billboard number one singles and collected thirteen Grammys

Have you noticed the key word hidden toward the end of the sentence, well away from the underline? Where examinees may be swayed into a Modifier distinction and then make a casual decision between the verb tenses in A and C, the astute test takers will recognize that “The Whole Sentence Matters” and see that word “since” waiting toward the end of the sentence. “Since” connotes an ongoing nature to the timeline of the sentence and therefore begs the word “has” in front of verbs to stay consistent with that timeline. So C has to be the correct answer. Where this sentence – and others with even more nuance and misdirection – has the power to distract you is in the fact that your mind wants to stay close to the underline and start to “check out” the further away you get from it. Savvy testmakers know this, and will hide small words well away from the underline, baffling novice test-takers and rewarding the astute ones who know to look for:

-Pronouns (it, they, their…)

-Words that signal time (since, after, until…)

-Connectors (but, or, and…)

When you’re struggling to make a decision, steal a page from Marshall Mathers and look toward the end of the sentence (the Aftermath?) to see if an important word or phrase makes a comeback to change the game. The GMAT loves to distract you by putting plenty of text in between the decision (the underlined portion) and the word that controls that decision. On harder questions, you’ll have to be patient and know to look for that word even all the way at the end of the sentence. Don’t lose yourself in the answer choices; let that tiny hidden word far from the underline be a major factor in your recovery.
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Looking for Similar Triangles on the GMAT [#permalink]
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FROM Veritas Prep Blog: Looking for Similar Triangles on the GMAT

Our Geometry book discusses the various rules we use to recognize similar triangles such as SSS, AA, SAS and RHS so we are assuming that we needn’t take those up here.

We are also assuming that you are comfortable with the figures that beg you to think about similar triangles such as

 



Try to figure out the similar triangles and the reason they are similar in each one of these cases. (Angles that look 90 are 90). Most of the figures have right angles/parallel lines.

This topic was also discussed by David Newland in a rather engaging post last week. You must check it out for its content as well as its context!

What we would like to discuss today are situations where most people do not think about similar triangles but if they do, it would make the question very easy for them. But before we do that, we would like to discuss a concept related to similar triangles which is very useful but not discussed often.

We already know that sides of similar triangles are in the same ratio. Say two triangles have sides a, b, c and A, B, C respectively. Then, a/A = b/B = c/C = k

Note that the altitudes of the two triangles will also be in the same ratio, ‘k’, since all lengths have the ratio ‘k’.

Then what is the relation between the areas of the two triangles? Since the ratio of the bases is k and the ratio of the altitudes is also k, the ratio of the areas will be k*k = k^2.

So if there are two similar triangles such that their sides are in the ratio 1:2, their areas will be in the ratio 1:4.

Now we are all ready to tackle the question we have in mind.

Question: In the given figure, ABCD is a parallelogram and E, F, G and H are midpoints of its respective sides. What is the ratio of the shaded area to that of the un-shaded area?



(A)   3:8

(B)   3:5

(C)   5:8

(D)   8:5

(E)    5:3

Solution: There are many ways to do this question but we will look at the method using similar triangles (obviously!).

Assume the area of the parallelogram is 8P. In a parallelogram, the lengths of opposite sides are the same. The two triangles formed by the diagonal and two sides are similar by SSS and the ratio of their sides is 1. So they will have equal areas of 4P each (look at the figures in second row below)



Now look at the original figure.

HE is formed by joining the mid-points of AD and AB. So AH/AD = AE/AB = 1/2 and included angle A is common. Hence by SAS rule, triangle AHE is similar to triangle ADB. If the ratio of sides is 1/2, ratio of areas will be 1/4.

Since area of triangle ADB is 4P, area of AHE is P. We have 3 such triangles, AHE, DHG and CGF which are not shaded so the area of these three triangles together will be 3P.

The total area of parallelogram is 8P and the unshaded region is 3P. So the shaded region must be 5P.

Hence, area of shaded region : Area of unshaded region = 5:3

Answer (E)

Try to think of other ways in which you can solve this question.

Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!

 
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School Profile: International Exploration, Tenting, and Pizz [#permalink]
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FROM Veritas Prep Blog: School Profile: International Exploration, Tenting, and Pizza at Duke University

Duke University is ranked #15 on the Veritas Prep Elite College Rankings. This research university is located on a 9,000 acre campus in Durham, North Carolina. It’s had three name changes and two campus location changes since its 1838 Quaker roots.

More than three-quarters of Duke students are involved in some type of service learning either locally or internationally in keeping with the university’s “knowledge in service to society” mission.

Duke University is divided into four colleges.

  • Trinity College of Arts and Sciences graduates nearly 80% of all undergraduate students. The college’s philosophy of immersing students in hands-on research prepares them to make significant contributions to their fields of study.
  •  Nicholas School of the Environment gives students the opportunity to prepare for careers in ocean sciences, earth sciences, and natural history through perspectives in not only science, but public policy.
  • Sanford School of Public Policy prepares students to be ethical leaders in the realm of public policy-making.
  • Pratt School of Engineering is one of the fastest growing engineering schools in the nation, offering undergrads degrees in electrical and computer, biomedical, civil and environmental, and mechanical engineering.
The new Bass Connections initiative organizes learning and research around problem-solving  rather than discipline. Multi-discipline teams work on specific problems that need to be solved. For example, one team has taken on the problem of environmental epidemiology in Latin America. They’re doing research in a small Peruvian village in the Amazon, and have brought together the disciplines of global health and environmental engineering. This is an example of the kind of hands-on research that turns students at Duke into global problem-solvers.

Duke is one of the few schools that require students to live on campus for three full years of their undergraduate studies. Incoming freshmen are assigned to one of fourteen residences based on their academic studies and interests. Students who opt to participate in the FOCUS program are housed together as well. Sophomores, juniors and seniors have more flexibility in their campus housing choices, but all are affiliated with one of the 80 houses on either the West or Central campuses. Each house determines its own personality. Co-ed selective living arrangements offer upperclassmen the choice to live in social groups that are outside the Greek system. Most are organized around a particular interest. Nine sororities and fifteen fraternities in the Greek system are housed on the Central campus.

Duke athletics are epic, especially the men’s basketball team (even though they lost to Mercer during March Madness this year), and Duke fans are matchless in their enthusiasm and support for the team. Since tickets to athletic events are free for Duke students, a practice known as “tenting” has become the norm. It’s basically a line to purchase tickets for games where students pitch tents in a row, making sure they have the correct amount of people in their tent to stay in line. Occasionally, the “tent village” will hold a concert or Coach Krzyzewski will buy pizza for the enthusiastic fans in the village.

Besides the tradition of tenting before big games, there are a few other interesting campus traditions. One is the unofficial graduation requirement of driving backwards around the campus traffic circle. Another requires students to climb Baldwin Auditorium. The Chapel Tower climb has been a long-standing tradition at Duke; the daring is increased by rumors of the chapel being haunted. A less dramatic and more noble tradition was recently begun where students now participate in academic homecoming ceremonies to honor their choice of majors. Students who crave a social environment and want to be part of something bigger than themselves may want to put Duke University on their top five list.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of ChicagoPomona College, and Amherst College, and more to see if those schools are a good fit for you.

By Colleen Hill
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The Most Efficient Way to Study Least Common Multiples on th [#permalink]
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FROM Veritas Prep Blog: The Most Efficient Way to Study Least Common Multiples on the GMAT

I recently had a student write in to ask me, “Can you explain to me the reasoning behind the Least Common Multiple? I understand that you take the prime factors from each number but I have no idea why. I think if I understood why I would be better at this technique.”

Let me see if I can make this concept more approachable for you. Think about calculating the Least Common Multiple as if you were a builder getting ready to build a house. The problem is you do not know which house you are going to build. So when you show up on the job site you need to have all of the materials for each of the possible houses. The “houses” are the numbers and the “materials” that you need are the prime factors.

Try this example (let’s use three numbers to make it more challenging):

What is the Least Common Multiple of 9, 20, and 42?

First you need to get the prime factors of each of the numbers. The prime factors of 9 are 3 * 3 the prime factors of 20 are 2 * 2 * 5 and the prime factors of 42 are 2 * 3 * 7.

Next you need to take each prime factor at the highest power. This is because you need to have all of the materials (prime factors) necessary to build any of the three houses (numbers). So your materials list is 2 * 2 * 3 * 3 * 5 * 7 or in other words 22 * 32 * 5 * 7. If you have these prime factors you can build any of the three numbers. For example, if you are asked to build the 20 you have the necessary 2*2*5.

Now you are also a very efficient builder so you do not want to bring more materials than you need. So you have to show up at the job site with the exactly the smallest load of materials with which you can build any of the houses. So that means that you do not want any extra prime factors. That is why the least common multiple on our example is 2 * 2 * 3 * 3 * 5 * 7. There is not a second 5 or another 7 because this is not needed.

You will not be asked to build more than one of the houses at any time. So even though if you list out the prime factors you will see three 2s (there are two of them in the 20 and one in the 42) and three 3s (two in the 9 and one in the 42) you do not need to bring all of these materials. You only need two 3s because you will only need to build the 9 or the 42 and not both. You only need two 2s because you will be asked to build the 20 or the 42 but not both.

I hope this helps to explain why you take each prime factor at its highest power. Understanding the reasoning behind the Least Common Multiple can help you to “build” a higher GMAT score.

Plan on taking the GMAT soon?  We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

 David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.
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SAT Tip of the Week: 4 Ways You Can Increase Your Reading Sc [#permalink]
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FROM Veritas Prep Blog: SAT Tip of the Week: 4 Ways You Can Increase Your Reading Score Right Now

In my tenure as an SAT teacher I have heard all explanations imaginable as to why the reading on the SAT is the most boring and awful reading in the known universe.  Students tell me the reading is too dense, too dry, too descriptive, too hard.

There is no arguing with the fact that some of the passages on the SAT are less than thrilling, but in order to score at the highest level on the SAT, students must find a way to stay present and actively consume the material.  There are a couple of techniques that can help with this process and allow students to answer questions about the passage effectively.

Make Short Summaries of Paragraphs Including What a Paragraph is DOING

This technique will not only help students to remember what content is covered in which paragraph (which is especially helpful for longer passages), but it will also prep students to have an answer ready when the SAT inevitably asks what the “purpose” of a paragraph or phrase is. Almost always, the purpose can be explained as “what is this language trying to accomplish?”.  Is it supporting a point of view? Discrediting a theory? Describing a memory?  If students can identify what a paragraph is doing, it will essentially give them a starting point to attack a question about purpose when it arises.

Ask Questions

If something seems strange, interesting, or even awful, identify it and ask why the author chose to phrase something in that strange, interesting or awful way.  It is likely that pieces of language that are unusual will be referenced in a question. For example, suppose there was a passage which contained the following sentence:

“There is no sin so decadent, so devious, so divine as the first instance of breaking a diet that has left you starved and broken.”

A student’s instinct should be to note this phrase and ask why the author chose to use it.  In this case the use of the words “sin” and “devious” with the words “divine” and “decadent” probably show that this action, which is considered bad, feels really good.  Doing this helps students to anticipate questions and be ready for them.

Translate Hard Sentences or Sections

Sometimes, all it takes to understand a difficult section is to translate some of the tough vocabulary.  The time and energy spent studying all those SAT vocab words will come in very handy in this endeavor. Say a question asked why the author used the following phrase:

“To be intractable was more than his whim: it was his modes-aparendi, and there was no dissuading him once an idea had him in his clutches.”

This phrase is a little dense, but mostly because of a few tricky vocabulary words.  “Intractable” just means stubborn, and “modes-aparendi” is Latin for mode of operation.  A “whim” means a momentary desire or thought, and “dissuade” is the opposite of persuade.  Let’s look at it again:

“To be stubborn was more than his momentary desire: it was his mode of operation, and there was no way to un-persuade him once an idea had him in its clutches.”

The passage is simply saying that this character is really stubborn.  Once the translation is done, it is easy to see what the true nature of the passage is.

Look for Answers While You Read

As students read the passage, they should refer back to the line specific questions as they are reading so that they are actively looking for the answers as they read. For example, imagine there was a  question relating to the following lines which we have already seen:

“There is no sin so decadent, so devious, so divine as the first instance of breaking a diet that has left you starved and broken. If there is, friends, I have yet to experience it!”

Now imagine the question asks the following:

“Which of these techniques is NOT utilized in lines 6-7 of the passage?”

            a) Alliterative language

            b) Hyperbole

            c) Religiously charged comparisons

            d) Verbal repartee

            e) Personal declaration

If a student encounters this question, he or she could simply start marking off what does and does not happen in the section of text referenced as he or she reads.  A quick glance shows there is alliteration (“decadent, devious, and divine all have the same first consonant sound”) and hyperbole (“starved and broken”) as well as religious comparisons (“no sin so…”) and a personal declaration (“I have yet to experience it”). Thus, the only technique NOT used is repartee as there is no other character to offer witty replies.

Reading actively can be a challenge, but is essential for a great score on the reading section. With a little practice, staying present in these passages will not seem like such a chore. In fact, students may even find themselves learning something new, or at least actively tearing apart some writing that they hate. Happy studying!

If you plan to take the SAT in a couple of years though, you will see a new SAT. Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.
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How to Write the Best Essay for Your MBA Applications [#permalink]
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FROM Veritas Prep Blog: How to Write the Best Essay for Your MBA Applications

Having graduated from a top MBA program as a non-native English speaker, I still remember being quite worried about the MBA application, fearing that my English was not sophisticated enough. So I focused on improving my writing skills by doing just that – writing.

Now as a Veritas Prep School Specialist, I have found working with my clients that there are a few common essay-writing pitfalls.

Here are some examples:

a)  Essays written in a generic way, which focus too much on current work experience. This is not a job application, so try to avoid producing what looks like a resume or CV in essay form.

b)  Essays that sound like a request for proposal (RFP), with an obvious Power Point sentence writing style with percentages, jargon and keywords such as “innovative” to impress Admission Committees. These committees have seen it all, so be innovative, don’t just say it.

c)  Essays that don’t talk about you. If an essay question asks what matters to you most and why, the essay will be an opportunity to demonstrate that you are inspired and motivated thanks to XYZ. This shows determination and focus.

Personal essays provide precious opportunities to reflect who you have been, where you want to go and your current plan to achieve this. It’s about showing a balance between early leadership aptitude and self-awareness. Use simple sentences but entice your reader by showcasing your talents, creativity and maturity, and this will help them to envision you enrolled in their MBA program.

These are 3 simple but powerful tips by advertising guru David Ogilvy from the book “How To Write”:

1)      Write the way you talk. Naturally.

2)      Use short words, short sentences and short paragraphs.

3)      Never use jargon words like reconceptualize, demassification, attitudinally, judgmentally. They are hallmarks of a pretentious ass.

Given that the business world does not usually demand essay writing or personal reflection, I would personally suggest keeping a personal journal or diary to practice writing about yourself, as well as to read both business and non-business oriented articles, such as those published in magazines like Harvard Business Review and The Atlantic.

Even if English is not your native language, the goal is to find your own unique voice and use writing as your instrument. Simply. Elegantly. You.

These are just some suggestions about how you can begin to approach the task of essay writing. Talk to an experienced Veritas Prep Consultant to see how we can help you write effectively to increase your chances for admission to the MBA program of your choice!

If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

This Veritas Prep Head Consultant received a BA in International Economics from UCLA, and went on to the Stanford Graduate School of Business to receive her MBA. Her specialties for helping students include low GMAT score, low GPA, multicultural marketing, and entrepreneurship.
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Follow This Strategy to Save Time on the GMAT [#permalink]
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FROM Veritas Prep Blog: Follow This Strategy to Save Time on the GMAT

There are certain numbers that will show up on every GMAT. Some of these numbers you need to be able to manipulate, and some others will just lie there like the rocks of Stonehenge: static and immovable. Numbers like π and √2, which can be converted into decimals but generally simply encumber the equation.

However, other numbers will show up and need to be inserted into an equation. Some of these numbers will show up on essentially every GMAT exam: numbers like 2, 10 and 100. Each of these numbers will show up in various questions and need to be multiplied, divided or factored out. Nevertheless, a number that will show up frequently is one that is oft overlooked: 60.

The number 60 is inescapable in everyday life. After all, there are 60 seconds in a minute and 60 minutes in an hour. Have you ever wondered why there aren’t 100 seconds in a minute? The answer is that 60 is divisible by almost every important small number you can think of: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 (hey, you forgot 60!). 100 is divisible by most of these numbers, but not by 3 or any of its  multiples. This is the primary reason we restart the count after 59 instead of 99.  Even the most die-hard imperial system user could see the value of adopting metric time (Remember this moment: 80 after 2:00 on April 43rd).

However, since we’re unlikely to change timing conventions (no matter how many signatures we get on Facebook), we’ll have to make do with calculating things using the number 60. Specifically, the GMAT likes using conversion problems to demonstrate mathematical proficiency. If you’re going at a certain speed per hour, how far will you go in 80 minutes? These questions can get increasingly difficult when translating times from minutes to hours, and the key is often multiplying or dividing by 60.

Let’s look at an example to underscore the importance of this number:

A space shuttle orbits the earth at about 8 kilometers per second. This speed is equal to how many kilometers per hour?

(A)   480

(B)   2,880

(C)   4,800

(D)   28,800

(E)    48,000

This is the type of question that can bait you into time-consuming calculations, whereas a shrewd test taker can gain valuable time by recognizing that this question is simply asking you to calculate a certain number by 60, and then multiplying it by 60 again (let’s do the time warp!). Even if a question asks you to change one unit into another, you can always do it step by step or all in one shot. There are many ways to solve this, but let’s begin with the detailed process so we make sure we don’t make any mistakes.

If the space shuttle orbits the earth at 8 kilometers per second  (you can replace this word by miles if you’re more comfortable), then how many kilometers will it cover in one minute? We can simply multiply 8 by 60 to get 480 kilometers/minute. This is the number in answer choice A, but it is not the correct answer as we’ve only covered a single minute, or about 1.67% of the hour. (There’s still a lot of spinning to go!). If we take the 480 km/minute and multiply it by 60 minutes, we will get to the number of kilometers /hour. 480 x 60 is not obvious, but you ignore the 0’s so it boils down to 48 x 6. Doing this longhand, we can get to 288, and then add back in the two zeros for a total of 28,800. This is answer choice D and the correct answer to this question.

If you followed that strategy, you would get the right answer, but you would miss many opportunities for shortcuts. One of the most glaring shortcuts is to forgo the two-step process and simply multiply the initial speed of 8 km/second by 3,600. This is 60 x 60, and represents the number of seconds in an hour. Since 60 is a number that shows up so frequently on the GMAT, it’s worth knowing that the square of 60 is 3,600 as you may be asked to convert from hour to second and vice versa. Multiplying 8 by 3,600 will also get you to 28,800 in one operation instead of two.

Furthermore, it is possible to solve this question using zero calculations, using the power of order of magnitude. Very simply, if you recognize that there are 3,600 seconds in an hour, and you’re going a little less than 10 kilometers per second, then your answer should be a little under 36,000 kilometers/hour. Since answer choice E is bigger than this, and answer choice C is about five times too small, the answer must be answer choice D. This strategy may be difficult to use if the answer choices are close together, however it is undoubtedly the fastest way to get the correct answer when the answer choices are spread out as they are in this question.

There are also multiple other ways to get the right answer here. One hybrid solution that is pretty intuitive is to multiply 8 kilometers/second by 60 to get 480 kilometers/minute, as we did in the very first step. From there you know you need to multiply 480 by 60 to get the speed per hour, but your trap options are 480 x 10 and 480 x 100, both of which are clearly incorrect at a cursory glance. By order of magnitude, you can again determine that the correct choice must be D.

As will all questions on the GMAT, there are multiple ways to get the right answer, but some question types show up over and over again on the test. If you’re prepared for the common types of problems and can solve them using a variety of solutions such as unit digit, order of magnitude and shortcut math, you’ll see your test score go from 0 to 60 (or 760) on test day.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.
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School Profile: These UC Berkeley Traditions Will Make You W [#permalink]
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FROM Veritas Prep Blog: School Profile: These UC Berkeley Traditions Will Make You Want to Apply

The University of California, Berkeley, also known as UC Berkeley and Cal, is ranked #20 on the Veritas Prep Elite College Rankings. Cal is a public research university founded in 1868, and located on a 1,232 acre campus overlooking San Francisco Bay. It is home to over 25,000 undergraduate students and 10,000 graduate students in 14 colleges, including professional schools and graduate programs.

Cal has long been known for student activism. In 1964 students began the Free Speech Movement in response to the university’s attempts to rid the campus of student political groups when they were active in the Civil Rights and Women’s Movements of the 1960s. UC Berkeley students have a long history of political involvement.

The oldest of the ten universities in the UC system, UC Berkeley boasts 72 Nobel Laureates and 11 Pulitzer Prize winners among its alumni, faculty, and researchers. The university, where excellence is the standard, offers 350 degree programs, including 106 undergraduate degrees. With a mix of liberal arts, research, and professional programs for students to choose from, the most popular majors by student enrollment are electrical engineering and computer science. The university is well-known for its political science department too. This top-notch research university offers students countless opportunities to be involved in meaningful research across the disciplines with some of the best minds in the country. Take note that Cal is one of two universities in the UC system that is on a semester schedule.

Campus life at UC Berkeley is what the student makes of it, but the opportunities for social engagement are nearly endless. Three-quarters of students live off-campus, and a full 90% are involved in Greek life. Besides campus dorms, the university sponsors 20 off-campus housing options. Students can choose from themed houses – LGBT, vegetarian, all-female and others, or choose by community size, small, medium, or large houses; students can also choose from sponsored apartments. There are 65 Greek campus affiliates – many with housing.

Where you choose to live may be one way to find your niche in this super-sized campus experience. Independent, self-motivated extroverts will find their niche here and thrive; introverts may find campus life at Cal overwhelming and indifferent. Cal is not the place to go if you need hand-holding, but if you’re confident in yourself and what you want, and you thrive on challenges, then Cal should be on your short-list.

The UC Berkeley Golden Bears are an NCAA Division I program in the Pac-12 Conference, and have 29 men’s and women’s sports teams. Athletic competitions are held at California Memorial Stadium, known for its fantastic views, Haas Pavillion, Evans Diamond, and Edwards Stadium. The storied Golden Bears have accrued 16 national titles and over 90 team titles in their athletic history. Their longstanding rivalry with Stanford University is a spillover of the academic rivalry between one of the best public universities and one of the best private universities in the country. In each sport, the rivalry is marked by “The Big (fill in the blank).” For example, in football it’s The Big Game, The Big Spike is in volleyball, and so on. The two schools play for The Stanford Axe in football every year. If you love sports or are Division I student-athlete material, you’ll find plenty of enthusiasm here.

Cal has a rich history of traditions, many of them centered around athletics. The Big C visible from Memorial Stadium was put on Charter Hill and has been inspiring Cal athletes and their fans since 1907; it is maintained by The Rally Committee. The California Victory Cannon on Tightwad Hill above Memorial Stadium is fired at the beginning of every home football game, after every home score, and at the end of each home victory. Oski, Cal’s athletic mascot, has appeared at every home game since 1941.

Big Game Week is the most popular tradition at Cal with all kinds of activities that precede The Big Game with rival Stanford. Card stunts in the Cal rooting section of Memorial Stadium have been spelling out witty and enthusiastic messages during games since 1908. The Stanford Axe that was captured at a baseball game in 1899 was held hostage by UC Berkeley for 31 years, only coming out annually to rally students for The Big Game; now the winning school takes it home each year. There are other traditions that continue at Cal, but many more than have gone by the wayside over the years. You may be a part of new Golden Bears traditions, if UC Berkeley is right for you.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of ChicagoPomona College, and Amherst College, and more to see if those schools are a good fit for you.

By Colleen Hill
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GMAT Tip of the Week: ASAP Test Taking Can Be Rocky (That's [#permalink]
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FROM Veritas Prep Blog: GMAT Tip of the Week: ASAP Test Taking Can Be Rocky (That's Your Freaking Problem)

As Hip Hop Month draws to a close in the GMAT Tip of the Week space, it’s time to pass the torch to the new school; while Eminem, Tupac, the Wu Tang Clan, and other classic acts have taught you some important lessons about the GMAT, it’s time for the young bucks to impart some wisdom. So today we bring you an important message from A$AP Rocky, Drake, and Kendrick Lamar, who will show you one of the most common (f****g) problems that test-takers encounter while taking the GMAT.

In their incredibly-vulgar but even-catchier track “F*****g Problems,” they refrain “I love bad b******s that’s my f*****g problem; and yeah I like to f***, I’ve got a f*****g problem”. And in doing so, they (we promise) tell the familiar tale of GMAT pacing gone awry:

GMAT test-takers far too often go through easy-to-moderate level problems “A$AP”, which leads to a Rocky performance. Why? Because we love hard problems, that’s our effing problem. We’re in such a hurry to save time for the hardest problems out there that we make silly mistakes on the problems we should get right, then dump far too much time into the problems – those bad b*****s – that we probably wouldn’t have gotten right anyway.

Try this – look at your next practice test and see how you allocated your time. Your quant performance, for example, might look like:

Time taken….Correct/Incorrect

1:47….Correct

1:58….Incorrect

1:22….Incorrect

1:45….Correct

3:05….Incorrect

1:12….Incorrect

1:58….Correct

1:50….Correct

2:58….Correct

Because of the way the GMAT scoring algorithm works, missing “easy” questions – perhaps by going through them ASAP and not spending that extra few seconds double-checking your work – hurts you substantially more than getting really hard questions correct helps you. After all, the system has to assume that it’s possible for you to guess correctly on 20% of the questions way above your head, so it can chalk that up to “probability”, whereas when you miss easy questions that’s just on you. And if you look at this sample section breakdown, that’s likely what the user did – spending 1:22 and 1:12 on “easier” problems (those that came after another incorrect answer) and getting those wrong, while spending ~3 minutes on “harder” questions and not really helping the cause. Even that correct answer at the end came at the expense of some valuable time and may well have been a guess (or could have been guessed correctly, anyway.

The problem that many GMAT students have – and it’s human nature, so you just need to be aware of it – is that they disproportionately spend their time on those “bad b******s” hard problems and go through the easier problems a little too ASAP. In doing so, they often make just enough careless mistakes on the easier questions that their score suffers mightily. So how can you fix that? Let’s borrow a line from A$AP Rocky as he opens the song in question:

“Hold up, b*****s simmer down…”

What he means, obviously, is to spend that extra 5-10 seconds on early problems to “hold up / simmer down” and double-check your work to make sure that you didn’t make a careless mistake or dive right into a trap answer. Those seconds are more valuable to you in rescuing yourself from a silly error than they are in attacking a problem that you probably wouldn’t have gotten right, anyway. ASAP answers can be rocky.

Now, you may be asking “okay, I’ll spend an extra 5 seconds per question double-checking my work, but what if I’m already short on time – where does that time come from?”. And the answer is this – most students struggle to comfortably complete the full section in 75 minutes, but most could complete most of that section – maybe 33-34 quant or 38-39 verbal questions – comfortably in that time. So rather than rush through all 37 / 41 questions ASAP leading to a rocky performance, learn from A$AP’s next lyric:

“Taking hella-long, b***, give it to me now”

Meaning, of course, on problems that would take you a hella-long time to answer, rather than spend 2-4 minutes en route to what might end up being a blind guess, anyway, make your guess now (and make that thing pop like a semi or a nine…). If you know you can’t comfortably answer all the questions in 75 minutes, give yourself 2-3 time-saving “I pass” questions per section, and when you see something that seems labor-intensive and outside your comfort zone, blow in your 20% shot at a guess and bank that 2 minutes to make sure you do your best work on the problems that you should get right. It’s better to do your best work on 34 quant questions and completely blow off 3 than it is to do 90% effective work on all 37, as silly little mistakes on the easier questions will significantly hold back your score. If you can get a question right, get it right.

Naturally, this takes practice to implement, and so it’s important to get a feel for your own pacing (ideally you never need to guess, but realistically most students do at some point). Which is why the Veritas Prep practice tests include pacing statistics per question (your pace vs. the average pace for all users) *and* a feature entitled “The Three Easiest Question You Got Wrong” to help you determine which types of questions require that extra 5-10 seconds to make sure you’re not leaving those easy points on the table. With any pacing or “triage” strategy, you’ll need to practice to see how it works for you, and if ‘finding a test that’s real is your f**** problem, bring your practice to our Item Response Theory tests and maybe we can solve it’.

Most importantly, recognize that one of the biggest f**** problems test takers have on the GMAT is going through problems ASAP and leaving themselves vulnerable to silly mistakes and a rocky performance. Don’t bank the time for those “bad b*****s”, the hardest problems out there; instead, hold up/simmer down, double-check for silly mistakes, and maximize your score. We hope this pep talk turns into a pep rally as you celebrate GMAT success.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin
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Determining the Area of Similar Triangles on the GMAT [#permalink]
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FROM Veritas Prep Blog: Determining the Area of Similar Triangles on the GMAT

Recall the important property that we discussed about the relation between the areas of the two similar triangles last week – if the ratio of their sides is ‘k’, the ratio of their areas will be k^2. As mentioned last week, it’s an important property and helps you easily solve otherwise difficult questions. The question I have in mind today also brings in focus the Pythagorean triplets.

There are some triplets that you should know out cold: (3, 4, 5), (5, 12, 13) and (8, 15, 17). Usually you will find one of these three or their multiples on GMAT. Given a right triangle and two sides, say the two legs, of length 20 and 48, we need to immediately bring them down to the lowest form 20:48 = 5:12. So we know that we are talking about the 5, 12, 13 triplet and the hypotenuse will be 13*4 = 52. These little things help us save a lot of time. Why is it that some people get done with the Quant section in less than an hour while others fall short on time? It is these little things that an adept test taker has mastered which make all the difference.

Anyway, let us go on to the question we have in mind.

Question: In the figure given below, the length of PQ is 12 and the length of PR is 15. The area of right triangle STU is equal to the area of the shaded region. If the ratio of the length of ST to the length of TU is equal to the ratio of the length of PQ to the length of QR, what is the length of TU?



(A) (9√2)/4

(B) 9/2

(C) (9√2)/2

(D) 6√2

(E) 12

Solution: The information given in the question seems to overwhelm us but let’s take it a bit at a time.

“length of PQ is 12 and the length of PR is 15”

PQR is a right triangle such that PQ = 12 and PR = 15. So PQ:PR = 4:5. Recall the 3-4-5 triplet. A multiple triplet of 3-4-5 is 9-12-15. This means QR = 9.

“ratio of the length of ST to the length of TU is equal to the ratio of the length of PQ to the length of QR”

ST/TU = PQ/QR

The ratio of two sides of PQR is equal to the ratio of two sides of STU and the included angle between the sides is same ( = 90). Using SAS, triangles PQR and STU are similar.

“The area of right triangle STU is equal to the area of the shaded region”

Area of triangle PQR = Area of triangle STU + Area of Shaded Region

Since area of triangle STU = area of shaded region, (area of triangle PQR) = 2*(area of triangle STU)

In similar triangles, if the sides are in the ratio k, the areas of the triangles are in the ratio k^2. If the ratio of the areas is given as 2 (i.e. k^2 is 2), the sides must be in the ratio √2 (i.e. k must be √2).

Since QR = 9, TU must be 9/√2. But there is no 9/√2 in the options – in the options the denominators are rationalized. TU = 9/√2 = (9*√2)/(√2*√2) = (9*√2)/2.

Answer (C)

The question could take a long time if we do not remember the Pythagorean triplets and the area of similar triangles property.

Takeaways:

  • Pythagorean triplets you should know: (3, 4, 5), (5, 12, 13) and (8, 15, 17) and their multiples.
  • In similar triangles, if the sides are in the ratio k, the areas of the triangles are in the ratio k^2.
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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Can I Get Accepted into Harvard, Stanford, or Wharton with a [#permalink]
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FROM Veritas Prep Blog: Can I Get Accepted into Harvard, Stanford, or Wharton with a 650 GMAT Score?

Yes you can.

But it becomes statistically less and less likely every year.  One thing is certain:  there are a lot of folks out there who have cracked the code on the formidable GMAT exam and scores continue to rise to stratospheric levels, pushing the average up of course.  Most schools publish the percentages of each level of the GMAT who gain admission every year, but these three schools, often considered the “holy grail” of b-schools, are exceptions.

They keep this information close to the vest and will only say that the GMAT is “very important” in the admissions process and state their median GMAT score each year (for each school it was in the low 700’s for class of 2015).   Based upon the published stats from other top schools, I believe it’s safe to say that not very many applicants with a 650 are getting in to these top three schools.  In fact, at other leading (top 10-ish) schools who do publish their percentages, fewer than 12% of the applicants have GMATs under 650 and fewer than 9% of admitted applicants have below that mark.

This puts you in a tight spot indeed if you are trying to get in with a 650.  Not only are there very few applicants who are admitted with that score, there are far more applicants who achieved that score than those who achieved higher.  Simply put, you are a small fish in a very big pond, and the odds of catching a baited hook are low.

A more telling statistic is their score range, which they do indeed publish and as of last year was 530-780 for Harvard, 550-760 for Stanford and 630-790 For Wharton.  So technically, you can get in these schools with only a score in the 500’s on the GMAT!  Don’t you feel relieved?  What the number doesn’t tell you is that the person who had the 530 also developed a cure for cancer, or built a post-atmospheric earth orbiting vehicle out of spare parts from their garage, or some other incredible feat.   Most schools publish an 80% range which gives a better idea at least of the probable range for most students.

The point, I guess is, the devil is in the details.  Can someone get into Stanford, Harvard or Wharton with a 650?  Yes indeed someone can.   Can YOU get in with your 650?  It all depends on the story behind the score.  Focus on what you have achieved that is extraordinary and what you offer that is unique and different than the average Stanford applicant (keeping in mind the “average” applicant to these super elite schools is pretty impressive), and at least you will have the best shot with that 650 that you can possibly have.  At the end of the day, these schools, with their large student bodies, are able to take the occasional flyer on the right person, regardless of GMAT score.  Perhaps that right person is you?  Best of luck.

If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

Scott Bryant has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons.
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School Profile: Create Your Dream Education at Middlebury Co [#permalink]
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FROM Veritas Prep Blog: School Profile: Create Your Dream Education at Middlebury College

Middlebury College is a small liberal arts college located in Middlebury, Vermont.  It is currently ranked #19 on the Veritas Prep Elite College Rankings. This is a top tier college for liberal arts and was founded in 1800; it’s known for international studies and leadership in language instruction. Students can choose from among 44 majors with over 850 courses.

Located between the gorgeous Green Mountains on the east and the Adirondacks on the west students will not only be inspired on a daily basis, but also have a natural research lab that surrounds them. The class sizes are kept small, usually around fifteen people, so students get an intimate educational experience. Middlebury is known for on-campus environmental initiatives as well as focusing on environmental issues around the world. Students who attend this college are expected to leave as leaders who are ethical and thoughtful.

Champlain Valley is known as the heart of Vermont and is also home to the student residences for those who attend Middlebury. They offer a variety of living options and strive to make their students feel safe and comfortable, ensuring that friendships are built and nurtured. There are a multitude of student activities and groups that students can participate in or be a part of. If you can’t find the organization you’re looking for among the 150 currently offered, feel free to create one of your own with the support of the Student Activities Team. Due to the expansive and rich outdoors, there are a wide variety of outdoor activities offered on campus from kayaking to winter camping. Campus life at Middlebury is all about enjoying the great outdoors, exploring and appreciating diversity, and building a strong community.

The academic program at Middlebury is designed to give each student a deep understanding of their defined major while also developing them into well-rounded individuals in various disciplines. The college places an emphasis on writing, which helps students to develop critical thinking while pursuing the requirements that give them a diverse education. At Middlebury students have a large amount of freedom to create their individual academic path due to the wide range of academic choices offered to them. There are a vast number of educational programs from study abroad to writing programs; at this college students really can create their dream education plans.

At Middlebury there are 30 NCAA varsity teams; more than 25% of the students play on one of the varsity teams. Middlebury has won countless National Championships in several of the different sports teams, from hockey to soccer. The campus has state-of-the-art facilities, including a golf course. There are off campus locations such as the Bread Loaf Mountain campus that serves as a ski touring center among other things. Middlebury does not just have excellent varsity sports teams, but is also committed to give all their students an opportunity to pursue good health by utilizing excellent gym equipment and engaging in many lifetime sports activities. Students are able to participate in the intramural programs and club sports programs that offer a wide range of recreational athletic activities.

Middlebury College started out as a small New England college built by a group of young men, and originally used to train young men in ministry and other related professions. A modest seven students attended this college the first year it was opened. It has know grown into a world renowned institute for liberal arts. This college is rich in history and tradition. The “Hunt” is a massive scavenger hunt in January and a favorite tradition to many. Students get personal with Senior Crush lists that display the seniors’ crushes from freshman year to senior year before they leave to join the real world. There are many more Middlebury traditions all year long; attending this college will allow you to participate in the fun.

We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter! Also, take a look at our profiles for The University of ChicagoPomona College, and Amherst College, and more to see if those schools are a good fit for you.

By Colleen Hill
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School Profile: Create Your Dream Education at Middlebury Co [#permalink]
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