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How to Improve GMAT Quant from Q49 to a Perfect Q51

A lot of people on the forum are not happy with their 79th percentile Q49 scores. These are good scores but understandably some just need a higher one to beat their competition. This guide is designed to be a comprehensive overview for very serious test-takers (those with Q49 already) 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 how to handle them. For the overview of what question types appear on the GMAT, see this post: overview-of-gmat-math-question-types-and-patterns-on-the-gmat-211809.html

1. Do I have to get ALL Quant questions right to Q51?

Answer: not all but you have to get to hard questions and to do that you have to answer 15-20 questions right in a row. Since GMAT Math is in a form of CAT (Compute Adaptive Test), the questions get harder if you correctly answer questions, and get easier when you get easy questions wrong. 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 difficulty and score of 50-51 usually appear after a question number 20. Therefore, it is crucial to get the first 20 questions right as otherwise you will not be able to get to hard enough questions to even get a shot at Q50/51.

2. What Concepts/Topics Do I Focus 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 most important 5 chapters. Among them, Integer Properties and Statistics are especially important. If you get every question right in “Integer section”, your score can go up as high as 49, and if you get every question right only in “Integer and Statistics section”, you can expect 50 for Math section. Thus, it is vital that you get every key question right from those five areas 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 of “different positive integers, median, mean, range, absolute value, and inequality” (that’s what we have seen on the test and what we keep hearing from our students). Answering it correctly or incorrectly will be the deciding factor, whether you get the perfect score or not – no second chances. These can be both PS or DS and they are especially hard in DS and you will have to solve them as they are designed to look deceivingly obvious or simple, for example have 3 variables but only 2 equations/data points. (Note: Math Revolution has a methodology that allows answering 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 designed this way on purpose.

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.

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.

Additional Practice: please try questions DS: #14 from OG15, or Question #121, #135 from OG 2016. (OG 2016 Quant directory).

Logic Questions – on the path to Q51, you will have to master Trick Questions or as we call them “Mistake Type” questions. If you get them wrong, the highest you can count on is Q49.

Side Note: What is a “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 Trap 1: If answer choice C seems too attractive and obvious, go back and check choice A or B alone. Look at the example below. What is the value of a and b ? 1) 2a + 6b = 8 2) 3b + a = 4 More practice in this C-trap collection c-trap-questions-177044.html

DS Trap 2: If an answer choice A or B seem too attractive and obvious, consider answer choice D. A good example is in this discussion

TIP! Important to note that 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 would be a good level “measuring stick” even for a person 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 Mistake Type/Trap 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 for DS. Besides the “Mistake Type”, one specific type of DS questions to master is Hidden Integer Questions. These questions often present prices of products, 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 question 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

Additional Practice: refer to OG15 DS: Question #132, OG16 DS: Question #47, #148, #150 and #153.

That is to say, among Mistake Types, there are many cases in which A or B easily seem like a right answer – but, in fact, D is a correct answer. In this case, 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

Additional Practice: please also refer to OG16 DS: Question #34 and Question #36.

In addition, You should be comfortable taclking 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 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 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?

→ 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 ths 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 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 to reach 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 experience of Max Lee. Due to the nature of the test and lack of transparency about the algorithm this guide is a best efforts 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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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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13 Dec 2015, 23:16

Hi, is there a short cut to find the answer to the 1st stats problem ?

I reduced statement 1 to 3a+b=24, where a<b<c and then substituted values, and concluded only 5,9,10 were possible. But this was only after I checked out the answer !

There is no short-cut to this question and you have to use substitution. This is because the number of variables and the number of equations do not match. An important strategy on the actual exam is to select which questions you are actually going to solve with caution. In other words, you have to select and focus. Also, it is important to take extra caution in solving questions like this one that involve Integers, Statistics and Positive Integers. So, even though C is a very attractive answer choice, A is the correct answer. Please remember that questions with a score range of 50 to 51 appear without notice.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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16 Dec 2015, 11:47

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I have noticed that the toughest questions on GMAT are DS questions on number properties, absolute value with inequalities, and probability with counting.

Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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25 Dec 2015, 13:21

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Can somebody please explain how statement B is sufficient in the below question:

Numbers a and b are positive integers. If a4-b4 is divided by 3, what is the remainder? 1) When a+b is divided by 3, the remainder is 0 2) When a2+b2 is divided by 3, the remainder is 2

We can get the answer by using only statement A, but what is the method used to prove that only B is also sufficient.

Hi, is there a short cut to find the answer to the 1st stats problem ?

I reduced statement 1 to 3a+b=24, where a<b<c and then substituted values, and concluded only 5,9,10 were possible. But this was only after I checked out the answer !

hi, we can cut down on timings by using a bit of logic.. the numbers you have taken are a,b,2a... we can work out the max value possible of a by taking b just one more than a.. so 4a + 1=24... or a=23/4=5.6 thus a's max value will be 5.. try with this number 5 and the largest =10... the middle term will become 9.... so this is one solution.. But are there any other values possible... NO why? the moment we decrease the value of a by one the largest number will exceed 2a.. so not possble
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Can somebody please explain how statement B is sufficient in the below question:

Numbers a and b are positive integers. If a4-b4 is divided by 3, what is the remainder? 1) When a+b is divided by 3, the remainder is 0 2) When a2+b2 is divided by 3, the remainder is 2

We can get the answer by using only statement A, but what is the method used to prove that only B is also sufficient.

Thanks in advance.

hi, lets see the second statement.. 2) When a2+b2 is divided by 3, the remainder is 2.. for this, you require to know that the square of any positive integer divided by 3 will leave a remainder of 1,if the int is not div by 3.. so if a^2 + b^2 is divided by 3, remainder is two.. only possiblity is both a^2 and b^2 leave a remainder of 1 each.. this would further mean a^2-b^2 will be div by 3....since remainder of 1 will get cancelled out eg 4^2-2^2=16-4=12... so overall answer is YES
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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29 Jan 2016, 19:13

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.

Can someone explain how is the OA for this A??

a,b,c must have unique values as DS always mandates. By statement 1 alone, A,B and C can have many values and not A SINGLE UNIQUE SET Of values that DS qs mandate.

Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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07 Feb 2016, 09:17

Just a quick question regarding you DS Trap #1

What is the value of a and b ? 1) 2a + 6b = 8 2) 3b + a = 4

How is the answer not C? As there are no restrictions as to what numbers a and b must be, one can easily find more than one example for each statement:

1) a=1 and b=1 matches the statement, but so does a=1/2 and b=7/6 --> insuff 2) a=1 and b=1 matches the statement, but so does a=-2 and b=2 --> insuff

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) A certain store, books are sold. Books are hard cover or soft cover and hard cover books sold $10 each and soft cover books sold $6. Is the number of hard cover books sold greater than that of soft cover books sold? 1) The average price sold of total books is $9 2) The number of hard cover books sold is 100

Furthermore, hidden integer questions of PS which lead to the score 50-51 are increasing. If you look at the question below, the number of coins is integer. Thus, this is a hidden integer question(the number of coins goes like 'one, two, three... and this is reason why it is a hidden integer question), which is a very recent question. Therefore, you should be prepared for hidden integer questions at all times to get them right.

(Example 2) A bank has a number of coins which equals $9.9 in total. There are only 2 types of coins: $0.1 each and $0.5 each. Which of thefollowing can be the number of $0.1 coins?

In addition, when it comes to the mistake types 3 and 4, simple questions are give like the past but sometimes difficult questions are gradually given. If you have a look at the example below, the answer is C but when applying the mistake type 4(A) as it is one of the key questions, which is an integer question. For 2), k=49 and m=4, n=15, which is unique and sufficient. Therefore, the answer is B.

(ex 3) Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is ‘0s’ number A and n is ‘4s’ number in set A, n=?

1) n>m 2) n=m+11

Hence, we also should be ready for the evolving questions as the mistake type 3 and 4 are being transformed and integer questions are particularly given frequently. When you face the questions, approach them deliberately. In that way, you will be able to hit a 51.
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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.

(ex 1) When x and y are integers, is x+y an even? 1) 2x+y is an odd 2) 5x+3y is an even Answer: B

The above question is also C but B can be the answer as well, which is a typically on the level of score 50-51 question. You should be strong on a question like this. Focus on integer or statistics questions, which make C an answer.
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Furthermore, inequality question in which you should always think of square are often given as the level of score 50-51.

(ex 2) Is \(1+x+x2+x3+x4<\frac{1}{(1-x)}\)? 1) x>0 2) x<1

Answer: C

On the above question, to modify the left and multiply (1-x)2 on the both equations is a critical factor for inequality questions. This question is on the level of score 50.
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Even for the mistake type 4 questions, they are becoming more complicated unlike simple questions in the past. For a question like the below, 1)=2), which is no and sufficient. Therefore, D is the answer.

(ex 3) If n is positive integer, is 3n+n2+1 not divisible by 3? 1) n is not multiple of 2 2) n is not multiple of 3

Answer: D

That is, questions are evolving like highly challenging questions, in which the mistake type 4 and 1 are combined. So, we should keep up with the evolving questions. In particular, integer questions are numerously given and you should carefully approach the questions, which will lead you to hit 51.
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