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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05 May 2016, 22:25

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You need to be extra careful on questions that involve the Common Mistake Type 4(B).

(ex 2) If x<0 and y<0, is x/y<1?
1) |x|<|y|
2) x>y
Answer: D

In the above question, we easily can find out that the condition 1) is sufficient. However, finding the condition 2) as the sufficient condition is not that easy. Hence, this is the Common Mistake Type 4(B) which states that we should consider the answer choice D if A or B seems too easily an answer. This type of question always appears in the score range between 50-51.

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Some of difficult questions are related to our daily lives. You need to get them right for the perfect 51.
A bank has a number of coins which equals $3.35 in total. There are only 2 types of coins: $0.25 each and $0.1 each. What is the remainder when the number of $0.1 coins is divided by 5?
I. 0 II. 1 III. 2
A. I only B. II only C. I & II only D. I & III only E. I, II & III
Answer: B

This type of questions seems simply, but they are rather quite challenging. We call this type of questions as hidden integer questions.

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As always, the more advanced questions combined with the Common Mistake Type 3 and 4 frequently appear in the GMAT Math. Let's have a look at the question below. It is one of the most current type of the question. This question can also be described as the question involving Common Mistake Type 4(B), which appears in the level of score 50-51. You have to be very confident with questions like this. You have to know the relationship between Variable Approach Method and the mistake types.

The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?
1) Event A and event B are independent.
2) The probability that neither event A nor event B occurs is 0.32.

From the original condition, we only have to know P(A∩B). Hence, there is only 1 variable in the original condition, making D the mostly likely answer. Using the condition 1) and the condition 2), we can see the condition 1)=the condition 2). Hence, D is the correct answer.

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This is a question related to the Common Mistake Type 4(A). You should be extra cautious on such type of questions.
If x, y are positive integers, what is the remainder when 2^(4x+2)+y is divided by 5?
1) x=3
2) y=1
Answer: B
Remainder questions that require you to divide the question by 5 has a cycle of 5. In other words, we get (~2)^1=~2, (~2)^2=~4, (~2)^3=~8, (~2)^4=~6.
Hence, the cycle of 4 is 24862486.
If we modify the original condition and the question, when we are dividing 2^(4x+2)+y by 5, we do not have to consider 4x. So, we need to consider only about 2^(2)+y. Since we only have to know y, the correct answer is B.

This is a type of questions that appears in the score range of 50-51.

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13 May 2016, 05:51

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This is one of the most challenging types of the question that looks like a journal. This is a PS question that you should be familiar with.

It is well-known that the way to find out approximation value of a positive integer n’s square root is following;
1st approximation: select a positive integer "a" and n is divided by a.
2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor.
What is the approximation positive integer n’s square root, in terms of a and n?
A. (a^2+n)/2a B. (a^2+n)/2 C. (a^2-n)/2a D. (a^2+n)/a E. (a^2+2n)/a
Answer: A
N=aQ, (a+Q)/2=(a+n/a)/2=(a^2+n)/2a

This type of questions looks very simple, but it is rather challenging. You should not underestimate the difficulty levels of PS questions (by the way this is a statistics problem).

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15 May 2016, 21:37

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As always, the more advanced questions combined with the mistake type 3 and 4 are frequently given on GMAT Math. Let's have a look at the question below, which is a current question. This question is also the mistake type 4(A), which is on the level of score 50-51. You have to be very confident with questions like this. You have to know the relation between approach method to variables and the mistake types. In particular, questions including number and ratio are frequently given, in which ratio is always an answer. The question below also contains 1) ratio and 2) number and the answer is A as well.

(ex 1) When x and y are integers, is x+y an even?
1) 3x+5y=even.
2) (x+1)2(y+1)2=even.

In the original condition, there are 2 variables. Hence, even though C could be the answer, considering the relationship between the Variable Approach Method and the Common Mistake Type, we can see that the condition 1) is always yes because x=y=even or x=y=odd. The condition is sufficient and the answer is A.

Answer: A

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There is an increasing number of geometry questions. For example:
A quadrilateral is inscribed in a circle as above figure. What is the measurement of ∠R?
1) The radius of the circle is 5
2) The line segment PS is equal to the diameter of the circle.
Answer: B
The central angle is twice the angle of circumference. PRS=90 degrees. Hence, the correct answer is B.

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18 May 2016, 16:35

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(ex 2) A, B are two sets whose elements are integers, A∪B represent union set of two sets A, B. Is each of the elements in the set A divisible by 3?
1) A∪B={13,17,31,47,52}
2) B={13,17,47}

Also, questions involving the Common Mistake Type 4(A) is very tricky.
(ex 2) A, B are two sets whose elements are integers, A∪B represent union set of two sets A, B. Is each of the elements in the set A divisible by 3?
1) A∪B={13,17,31,47,52}
2) B={13,17,47}
Answer: A

There are questions that involve both the common mistake type 1 (no is also an answer) and the common mistake type 4(A). In above question, C is also an answer. If we look at that condition 1), even if A’s elements are any numbers, it cannot be divided by 3. The answer is no and the condition is sufficient. Therefore, the correct answer is A.
This is a type of questions that appears in 50-51.

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Also, there are statistics questions that involve the Common Mistake Type 4(A).
There are two kinds of books: hard-covers and paper-covers, if the range of the prices of both kinds of books is $50 and the range of the prices of paper-cover is $10, what is the range of the prices of the hard-cover books?
1) The lowest price of hard-cover books is $2 less than the highest price of paper-cover.
2) The highest price of hard-cover books is $40 more than the highest price of paper-cover books.
Answer: A

There are 4 variables and 2 equations. Hence, C can be an answer but since this is a statistic question, one of key questions, we need to apply the Common Mistake Type 4(A). The condition 1) is sufficient by itself, and the correct answer is A. You need to be strong at this type of questions to get 51.

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22 May 2016, 17:34

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As mentioned above, questions related to Murphy’s Law and Sally’s Law might appear in the GMAT test.
You need to get them right if you are aiming for the perfect 51!

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As always, there are questions that is combined with the common mistake type 3 and 4. Let’s take a look at a question below. This is a 50-51 level question and is a question that involves the common mistake type 4(A). You need to be strong at these questions and have to know the relationship between the Variable Approach method and the Common Mistake Types.

If x, y, and z are integers greater than 1, x+y+z=?
1) xyz=154
2) x-y-z=2

There are 3 variables (x,y,z) in the original condition. In order to match the number of variables to the number of equations we need 3 equations. Hence, there is high chance that E is the answer. Using both the condition 1) and the condition 2), we get 11, 2, 7. The answer is unique and the condition is sufficient. Hence, the correct answer MIGHT be C.
However, since this is one of key questions, integer question, we need to apply the common mistake type 4(A). If we use the condition1 ), we get 11,2, 7. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

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Be careful on probability questions.
2 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
A. 12 B. 15 C. 18 D. 21 E. 24

Answer: A

Since, 3!*2!=12, the answer is A. This is a type of questions that appear in the 50-51 range.

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You also need to be careful on probability questions that involve “at least” like below.
In a certain factory the production line which produces the bulbs has the probability that a bulb selected at random is defective is 0.01. If 10 bulbs are selected at random, what is the probability that at least one bulb is defective?
A. 0.0110 B. (0.01)(0.99)10 C. 1-(0.01)10 D. 0.9910 E. 1-(0.99)10

Answer: E
Since the question asks what is the probability of 10 bulbs, selected at random, are all “no defective”, the answer is E.

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Also, there is a statistic question like below.
If the heights’ range of men is 14 inches and the heights’ range of women is 10 inches, what is combined heights’ range?
1) The shortest man is 3 inches shorter than the tallest woman.
2) The height of highest man is 72 inches.
Answer:A
There are 4 variables and 2 equations (14=MT-Ms, 10=WH-WS), in the original condition. In order to match the number of equations and the number of variables, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and the condition 2), C is the answer. However, this is a statistic question, one of the key questions. Hence, we need to apply the Common Mistake Type 4(A). We can see the condition 1) is sufficient by itself, making A and correct answer. Be careful on this type of question.

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There are many probability questions nowadays. You should be careful on these questions.
A certain jar has total 8,000 red marble, blue marbles, and green marbles. And the red marbles’ number is twice the blue marbles’ and the green marbles’ number is 20 more than the sum of red and blue marbles. If one marble is selected from randomly the jar, what is the probability that marble selected is red?
A. 133/400 B. 131/400 C. 129/400 D. 127/400 E. 137/400
Answer: A

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30 May 2016, 19:51

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Also, When (10^100)^20 have n consecutive 0-digits from units digit, what is the greatest possible value of n?
A. 1040 B. 10400 C. 1002 D. 1020 E. 10400
Answer: A
This is a PS question but in the score range of 50-51. Since 100^20=10^40, the correct answer is A.

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31 May 2016, 02:44

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if xy+z=x(y+z), which of the following must be true

1 x=0 & y=0

2 x=0 & y=1

3 y=1 & z=0

4 x=1 & y=0

5 x=1 & z=0

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Below is another 50-51 question.
On the number line m, s, t are there. If t and m are positive, is m=t?
1) |t-s|=|m-s|
2) s<0
Answer: C
There are 3 variables in the original condition (m, s, t). In order to match the number of variables and the number of equations, we need 3 equations. Hence, there is high chance that E is the correct answer. Using the condition 1) and the condition 2), the absolute values designates the distant between two points. Hence, the correct answer is C.

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05 Jun 2016, 06:22

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If x is an integer less than 11 and n is a positive integer, is x a prime number?
1) x2=n!+1
2) x=2n+1
Answer: A
This is also a 50-51 level question. There is 1 variable (x) in the original condition and there is high chance that D is the answer.
For the condition 1), n=4(x=5), n=5(x=11), the answer is always yes, and the condition is sufficient.
For the condition 2), x=5 yes, x=9 no. The condition is not sufficient, and the correct answer, thus, is A. This would be the hardest level question among 50-51 level questions.

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It is well-known that the way to find out approximation value of a positive integer n’s square root is following;
1st approximation: select a positive integer "a" and n is divided by a.
2nd approximation: a positive integer n’s square root is the average (arithmetic mean) of a quotient and divisor.
What is the approximation positive integer n’s square root, in terms of a and n?
A. (a2+n)/2a B. (a2+n)/2 C. (a2-n)/2a D. (a2+n)/a E. (a2+2n)/a
Answer: A

This is a thesis=like question. It is a very challenging 50-51 level question. N=aQ means √n=(a+Q)/2. Hence, the correct answer is A.

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