How to Improve GMAT Quant from Q49 to a Perfect Q51 Updated on Aug 28th, 2020 Many people on the forum are not happy with their 79th percentile Q49 scores. These are good scores, but understandably some require a higher score to beat their competition. This guide is designed to be a comprehensive overview for serious test-takers (those who previously achieved Q49) who are looking to get to the elusive Q51. Important: You only have one shot at the Q51 on your test. You will face a handful of elite questions and you need to be ready to face them. Here is a detailed inventory of the tough Q51 question types, concepts, and tips on how to handle them. For an overview of what question types appear on the GMAT, see this post: https://gmatclub.com/forum/overview-of- ... 11809.html 1. Do I have to get ALL Quant questions right to Q51? Answer: You do not have to answer all questions correctly; however, you must reach the hard questions, which is accomplished by answering 15-20 questions correctly in succession. Since the GMAT Math exam is in CAT form (Computer Adaptive Test), the questions increase in difficulty as you correctly answer questions, and get easier when you answer easy questions incorrectly. Therefore, after answering the first 7 questions correctly, you can expect your score to be around 35-40. These first few questions will be fairly basic and straightforward. In fact, you will have to keep going for a while, as the questions that are representative of a score of 50-51 usually appear after question number 17. Therefore, it is crucial to get the first 17 questions right as otherwise, you will not be able to reach the challenging questions that provide the opportunity to attempt achieving Q50/51. 2. What Concepts/Topics Do I Focus on when Targetting Q51 Score? Overview: It is vital to note in preparation for GMAT Math that Integer Properties, Statistics, Probability, Inequality, and Absolute Value are the 5 most important topics (Key Topics) that account for 60% of the GMAT math questions, and 80-90% of 50-51 level questions. Among them, Integer Properties and Statistics are especially important. If you get every question right in the “Integer” section, your score can go up as high as the mid-40s, and if you get every question right in the “Integer and Statistics” sections, you can expect to achieve a score in the high 40s for the Math section. Thus, it is vital that you correctly answer every key question from these five topics to score a 51. Integer Properties and Statistics . One question format in particular that keeps reoccurring is a question with a combination of 2 or 3 concepts of “different positive integers, median, mean, range, absolute value, and inequality” (that is what we have seen on the test and what we continually hear from our students). Answering it correctly or incorrectly will be the deciding factor in whether you get the perfect score or not – no second chances. These can be both PS or DS questions, and they are especially challenging in the DS section, as they are designed to look deceivingly obvious or simple, for example, questions dealing with 3 variables but only 2 equations/data points. (Note: Math Revolution has a methodology that provides you the knowledge required to answer up to 80% of easy/medium DS questions without solving them by matching the number of variables and the number of equations). It is not easy to solve these types of questions in just two minutes and they are purposely designed this way. Here are 2 examples of the Statistics and Integer Questions: Statistics: There are 3 different positive integers. If their average (the arithmetic mean) is 8, what are their values? 1) The largest integer is twice the smallest integer. 2) One of them is 9. →The correct answer is A . Integer Properties: The smallest of 7 positive integers is 1. Is the range of them greater than 3? 1) The average (the arithmetic mean) of them is 4. 2) The median of them is 4. → The correct answer is A . Logic Questions – On the path to Q51, you must master answering Trick Questions or, as we call them, “Common Mistake Type” questions. If you answer these questions incorrectly, the highest you can achieve is Q49. Side Note: What is a “Common Mistake Type” Trap Question? There are 5 types of questions that GMAT Math test makers design to trap students. Here are 2 of the most commonly used on the DS: DS Common Mistake Type 4 (A): If answer choice C seems too attractive and obvious, go back and check choice A or B alone. Look at the example below. If m and n are integers, is mn even? (1) m = 5. (2) m and n are consecutive integers. → The correct answer is B . DS Common Mistake Type 4 (B) If answer choice A or B seems too attractive and obvious, consider answer choice D. Look at the example below. If a, b, c, and d are different positive odd numbers, what is the median of the numbers? (1) a + b + c + d = 16. (2) The product of 3 numbers of a, b, c, or d is 15. → The correct answer is D . TIP! Important to note that the GMAC likes to use DS questions as the deciding factor for their Q50/Q51 scores…. most likely because DS questions are unique to the GMAT and thus provide a good level “measuring stick” even for individuals with a strong quantitative background. Therefore, if you are looking to score Q51, you will need to pay especially careful attention to the DS questions and learn how to spot Common Mistake Type questions. 3. Analysis of Specific Question Types to Master for Q51 DS Tips: As mentioned above, Integer and Statistics are the main chapters to focus on DS. Besides the “Mistake Type”, one specific type of DS questions to master is Hidden Integer Questions. These questions often present prices of products, the number of fruit, coins, people, stamps, cars, etc as “hidden integers”. These are countable numbers that are not given to increase complexity. These are logic questions and you should solve them logically rather than calculation. It is possible to calculate and solve these questions that way but it takes much longer and a lengthy calculation is exactly the trap the test wants to catch you with – to waste your time and slow you down. Integer Properties: M bought several pencils. If each pencil cost either 23-cent or 21-cent, how many 23-cent pencils did M buy? 1) M bought a total of 6 pencils 2) The total price of all pencils M bought was 130 cents → The answer choice C is very attractive, but the correct answer is B . Pencil is a hidden integer, but if you don’t recognize this fact, you would say C is the answer. In addition, Statement 1 is actually not giving you any helpful information Among Common Mistake Type questions, there are many cases in which A or B easily seems like a correct answer – when, in fact, D is the correct answer. One or two questions of this type play a decisive role in leading to a perfect 51. Integer Properties: Numbers a and b are positive integers. If a^4 - b^4 is divided by 3, what is the remainder? 1) When a + b is divided by 3, the remainder is 0. 2) When a 2 + b 2 is divided by 3, the remainder is 2. → The correct answer is D . In addition, You should be comfortable tackling inequality problems such as “greater than” and “less than” questions if you want to get a perfect 51. You should practice these so that your mind clicks when asked to figure out the minimum value (if asked “greater than”) and the maximum value (if asked “less than”). Statistics: There are five homes. If the median price of a home is $200,000, is the range of all prices greater than $80,000? 1) The average price of the five homes is $240,000. 2) Three of the five homes have the same price. → C looks like a right answer choice at first. However, the correct answer is A . Of course we would be incomplete if we did not include the famous DS Probability questions that you are likely to see on your quest to Q51. Here is an example: Probability: There are only apples and oranges in a box. What is the probability that the fruit selected at random from the box is an apple? 1) There are 2 apples in the box 2) The ratio of the number of apples to the number of oranges is 1 to 4. → C looks like a right answer choice, but the correct answer choice is B . In case of Absolute Value questions, a question regarding the relationship among |a|, a, and -a will determine a perfect 51. Absolute value: If |r|>|s|, is r>s? 1) r>0 2) s>0 → C is an attractive answer choice but A is a correct answer. Problem Solving Tips Be prepared to see questions about finding Hidden Integers and problems on the so-called “Pigeonhole Principle”. You have a good chance of seeing one of them. We have provided the definition of the Hidden Integer questions above in the DS section. Tip: if you see integer questions just like the number of fruits, people, animals, stamps, and candies, it is a good chance you are facing this question type. The name of Pigeonhole principle comes from the old problem of having to calculate the number of cases of pigeons entering pigeon lofts. (it will more clear once you read the example below). Integer Properties: There are 10 red balls, 10 blue balls, and 10 white balls in a box. What is the maximum number of balls you can draw from the box and have fewer than 5 balls of the same color drawn? A. 4 B. 5 C. 6 D. 10 E. 12 → This question asks for the maximum number of balls you can have, so the correct answer should be the unluckiest case. If you draw 4 red balls, 4 blue balls and 4 white balls all together, there can be no more than 4 balls of the same color. Hence, the correct answer choice is E . Questions related to Murphy’s Law and Sally’s Law are the questions for a perfect 51 in PS. * (Integer) There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks? A. 5,15 B. 4,15 C. 5,10 D. 4,10 E. 5,20 → D is the correct answer choice. Can you figure out how to solve it quickly? Good – remember this approach so you can refer to it on your test. 5. Conclusion In this way, a perfect 51 is not an outcome of luck; you have to concentrate to excel in Integer and Statistics parts to that end. Especially, DS questions often will be the determining factor of a perfect Q51, and, therefore, you should not be misled by Mistake types. Please pay special attention to the Mistake type questions. Please remember solving 37 questions in 75 minutes in the actual GMAT exam is a big challenge. You will need to manage time effectively to solve hard questions in 2 minutes or less per question. How can you reduce the time spent per question significantly? Since GMAT is a logical test, you should not question whether you can solve a problem or not, but you should practice reaching answers logically without having to solve problems. *** We are math experts and if you find any grammatical issues – that is because we spend all of our time focusing on math; sorry grammar. Note that the information herein is based on the knowledge and experience of Max Lee, who taught 30,000+ students and solved 100,000+ problems in the past 15 years. He discovered and analyzed types of GMAT Math questions after continuous and numerous interviews with students who have achieved a score of 49 to 51 in the actual GMAT exam. Thus, please note that the information is herein is based solely on the experience of Max Lee. Due to the nature of the test and lack of transparency about the algorithm this guide is a best-effort attempt based on the best information available. If you have any questions or different information, please post it here for the benefit of the community.

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There are questions that combine common mistake types 3 and 4. Below is a question type that frequently appears in the current GMAT test. This is a 50-51 level question that includes the common mistake type 4(B). You have to be strong at these types of questions. In order to solve it, you have to know the relationship between Variable Approach Method and the common mistake type.

(ex 1) When 25 integers are there such that their average (arithmetic mean) is 100, is their median equal to 100?
1) They are consecutive
2) The average (arithmetic mean) of the greatest number and the smallest number of them is 100

This is a typical common mistake type question that makes C and A both the answers.
Answer:A

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Geometry question like below is also very challenging.
(ex 2) At least 10 cars have tinting window and fog light. 40% cars which have tinting windows also have fog light, is the number of the cars with tinting windows larger than that of the cars with the fog light?
1) 80% cars which have fog light also have tinting windows
2) 52 cars have tinting windows or fog light or both

Question like above has one condition as a number and the other as a ratio. Then, the condition with ratio becomes the answer, making A the correct answer. This is a 50-51 level question.
Answer: A

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Be careful on a question that involves common mistake type 4(A) like below. These questions often involve integers.
(ex 3) There are 7 consecutive integers. How many multiples of 6 are in the 7 numbers?
1) The median of the 7 numbers is a multiple of 6
2) The average (arithmetic mean) of the 7 numbers is 12

Answer: D
Consecutive integers questions are also 50-51 level questions. Also ,these are common mistake type 4(B) questions.

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Below is another 50-51 level question.
For 2-by-2 question, if a percentage appears, then that condition is sufficient (This is only true when the question is in %).

As you can see, this is a 2-by-2 question, and the question is in %. Since the condition 1) and 2) each has one percentage, there are 3 percentages. Hence, the correct answer is D. This is a very challenging 50-51 question.
Answer: D

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There are some difficult PS questions that appear as 50-51 level questions.
In the x- y plane, there are 4 points (0,0), (0,4), (6,4), and (6,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A. 1/2 B. 1/3 C. 1/4 D. 1/5 E. 2/5
Answer: B
If we draw conditions on coordinates, the correct answer is B.

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MathRevolution can you please elaborate the solution B

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Also,
Is x<3?
1) 0.025(10x)<25
2) 0.025(102x)<250,000
Answer: A

This is a question involving inclusion relationships. If the range of the question includes the range of the condition, then the condition is sufficient. In this case, A is the correct answer.
(Since there is 1 variable, there is high chance that D is the correct answer. Hence, we should use the condition 1) and the condition 2) separately.

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Below is 50-51 question type.
If the average (arithmetic mean) height of John, Tom and Sue is 1.70m, what is the median height of them?
1) The height of Tom is 1.65m.
2) The height of Sue is 1.70m.
Answer: B

There are 3 variables (J,T,S) and 1 equation (J+T+S=5.1) in the original condition. In order to match the number of variables to the number of equations, we need 2 equations. Hence there is high chance that C is the correct answer. Using the condition 1) and the condition 2), C can be the answer. However, since this is statistics question, we need to apply common mistake type 4(A). The condition 2) always gives us median=1.7. Hence, the correct answer is B.

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MathRevolution can you please elaborate the solution B

Here is an answer to your question! Please refer to the attachment

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If x and y are integers, is xy an even?
1) x+3 is an even
2) y-3 is an odd
Answer: B

This is a recent 50-51 level question type.
As you can see, this is one of common mistake type 4(A) question in which both C and B can be the answer.

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If ab≠0, is |a^b|=a^b?
1) |a|=a
2) |b|=b
Answer: A

The above question can have 2 answers – C and A. For such questions, A becomes the correct answer. This is common mistake type 4(A) question.

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As always, questions combined with the mistake type 3 and 4 are given. Let's have a look at the example below. This is a very recent question, which also belongs to the mistake type 4(A). This question is on the level of score 50-51. You should be able to tackle a question like this. In addition, you should be aware of relation between approach method to variables and the mistake types.
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?
1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
2) The sum of the 3 numbers is equal to 3 times median of the 3 numbers.

If we assume the original condition as a<M<b. Then, the question becomes (a+M+b)/3=M?. Then, a+M+b=3M?. This is same as the condition 2), hence it is sufficient. Condition 1), b-a=2(b-M), is also yes. Hence, according to the common mistake type 4(B), the correct answer is D.

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Sometimes geometry question can be a high level question
A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch?
A. 54
B. 64
C. 81
D. 108
E. 120
Since 6*27-6*9=108, the correct answer is D.
This is always a type of 50-51 level question.

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Please be careful on common mistake type 4(A) question. Integer questions often appear as common mistake type 4(A) questions.
The product of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n is 54, what is the value of n?
1) n>950
2) The sum of the units digit, tens digit, and hundreds digit of a positive 3-digit integer n is 16.

Answer: A
There are 3 variables and 1 equation. Hence, there is high chance that C is the correct answer. However, we have to consider common mistake type 4(A) because it is integer question. Since the condition 1) gives us n=961, it is sufficient alone. So, the correct answer is A.

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In a certain school, 40% of all the students are boys. What percent of all the students take Biology?
1) All the students are 4,000
2) 10% of the girl students and 15% of the boy students take Biology
For a question like above, there are number and ratio. There is not exceptional case to this type of questions. In case of 2-by-2 questions, when % appears 3 times, that condition is sufficient (only when the question asks for %).
Girls Boys
Bio
NOT Bio
This is 2-by-2 and the question is asking %. Since the condition 2) has 2 % and there are 3 %, the correct answer is B. This is a very difficult question.
Answer: B

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Also, this is a challenging question.
n and k are positive integers. If n=(22)(3)(53)/15k, is n<k?
1) n<10
2) k>4
Answer: A

If we modify the original condition and the question, we get n=100/k. This means k=100/n. If we substitute, we get n<100/n?, n^2<100?. Hence n<10?. So, the correct answer is A.

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Below is also 50-51 question.
When x and y are integers, x^3y^4=z, x=?
1) z=2,000
2) y=2
Answer: A
There are 3 variables (x,y,z) and 1 equation (x^3y^4=z) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, there is high chance that C is the answer. Using 1) and 2), C can be the answer. However, if we apply common mistake type (4A), as this is an integer question – a key question, we get x=5 and y=2. The condition 1) is sufficient and the correct answer is A.

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If the average (arithmetic mean) of 9 numbers is 43, what is the standard deviation of them?
1) The smallest number of them is 43
2) The greatest number of them is 43
Answer: D
Above is also a 50-51 level question.
If Range=0, Max=mean, or min=mean, SD=0. In case of this question, (DS) mean=43.
1) min=43=mean
2) Max=43=mean

Hence, the correct answer is D.

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In addition, the mistake type 4(A) questions related to our life are given at level of score 50-51. In a case of the question below, the answer is A if you modify the question.

(ex 3) Machine X is taken 30 minutes for preparing to work and machine Y is taken 20 minutes for warming up before driving machines. The work rate of machine X is 40 parts per 1 minute and machine Y is 30 parts per 1 minute. Is the total time taken to work including preparing time of machine X smaller than that of machine Y?

1) The total task is more than 1,200 parts.
2) The total task is less than 1,800 parts.

Therefore, when you face with questions related to real life, approach them very cautiously.

MathRevolution Could you please post detailed solution for the problems,which you have been posting :-D

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As always, questions combined with the mistake type 3 and 4 are given. Let's have a look at the example below. This is a very recent question, which also belongs to the mistake type 4(B). This question is on the level of score 50-51. You should be able to tackle a question like this. In addition, you should be aware of relation between approach method to variables and the mistake types.
(ex 1) If s, p, t are there such that s<p<t, is the average (arithmetic mean) of s and t equal to 4p?
1) The average (arithmetic mean) of s, p, and t is equal to three times the median of them
2) s+t=8p
This is a common mistake type question in which both C and D can be the answer. This is 50-51 level question. If we modify the original condition and the question, we get (s+t)/2=4p? s+t=8p?. Hence, 2) is sufficient and in case of con 1), we get (s+p+t)/3=3p, s+p+t=9p, s+t=8p. Since 1)=2), the correct answer is D.

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