Ask me Anything about GMAT Data Sufficiency Hello, I am Max Lee, Founder and Lead Math Tutor at Math Revolution. We have over 9,000 posts and over 10,000 Kudos. This topic is a new feature on the DS Forum and a way for you to directly interact with our math team and ask anything about the DS, e.g. if you want a certain concept explained or have a particular question you want to us address, this is the place to post a link to it or your question. I intend to have this thread be as an "Everything You Need to Know about DS" type of thread. I will keep updating this post with links and resources that are helpful for the DS. Meanwhile, you can ask me anything Other discussions you may be interested in: How to Improve GMAT Quant from Q49 to Q51 - the Ultimate Q51 Quide Overview of GMAT Math Question Types and Patterns on the GMAT We will be posting new questions in this topic regularly - check it out for some new material! Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum! - Max Lee.

=> Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 1 variable ( n ) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) n could be any of the integers 1, 2, 4, 5, 7, 8, … If n is one of 1, 4, 7 , then n has a remainder 1 when it is divided by 3 . If n is one of 2, 5, 8 , then n has a remainder 2 when it is divided by 3 . Thus, condition 1) is not sufficient, since it does not yield a unique solution. Condition 2) n = 9k +7 can be expressed as n = 9k + 7 = 9k + 6 + 1 = 3(3k+2)+1 . Therefore, n has remainder 1 when it is divided by 3 . Thus, condition 2) is sufficient. Therefore, B is the answer. Answer: B

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27 Feb 2019, 05:43

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n is a positive integer. What is the remainder when n is divided by 3?

1) n^2 has remainder 1 when it is divided by 3
2) n has remainder 7 when it is divided by 9

We need to find r when n=3q+r

Statement 1: \(n^2\)=3q+1
By plugging in numbers, \(n^2\)= 1, 7, 10, 13, 16....25... => n= 1, \(\sqrt{7}\), \(\sqrt{10}\), \(\sqrt{13}\), 4.....5....
Plug in any value of n in n=3q+r. We get more than one value for r. NOT SUFFICIENT

Statement 2: n=9q+7
n= 7, 25, 34, 43..........
By plugging in any value of n in the eq. n=3q+r, you'll get r=1. SUFFICIENT

IMO the answer is option B.

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Updated on: 30 Dec 2021, 01:15

Originally posted by MathRevolution on 28 Feb 2019, 07:17.
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If n is an integer, is (n+1)(n+2)(n+3) divisible by 12?

1) n is an even number.
2) n is a multiple of 4.

Answer: B

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since n+1, n+2 and n+3 are three consecutive integers, (n+1)(n+2)(n+3) is a multiple of 3.

Condition 2) tells us that n+1 and n+3 are odd integers, and n+2 is an even number which is not a multiple of 4. Thus, (n+1)(n+2)(n+3) is not a multiple of 4.
CMT(Common Mistake Type 1) states “no” is also an answer and a condition giving rise to the unique answer “no” is sufficient. Thus, condition 2) is sufficient.

Condition 1)
If n = 2, then (n+1)(n+2)(n+3) = 3*4*5 = 60 is a multiple of 12 and the answer is “yes”.
If n = 4, then (n+1)(n+2)(n+3) = 5*6*7 = 210 is not a multiple of 12 and the answer is “no”.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Therefore, B is the answer.

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28 Feb 2019, 07:23

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Is x = y?

1) x ≤ y
2) |x| ≥ |y|

Answer: E

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Updated on: 08 Nov 2021, 02:11

Originally posted by MathRevolution on 01 Mar 2019, 00:55.
Last edited by MathRevolution on 08 Nov 2021, 02:11, edited 1 time in total.

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n is a positive integer. What is the remainder when n is divided by 3?

1) n^2 has remainder 1 when it is divided by 3
2) n has remainder 7 when it is divided by 9

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01 Mar 2019, 00:56

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[GMAT math practice question]

(number properties) If \(m\) and \(n\) are prime numbers, is \(m^2 + n^2\) an even number?

\(1) m > 10\)
\(2) n > 20\)

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[GMAT math practice question]

(number properties) If \(m\) and \(n\) are prime numbers, is \(m^2 + n^2\) an even number?

\(1) m > 10\)
\(2) n > 20\)

It is given that both m and n are prime numbers. We need to find whether \(m^2 + n^2\) an even number or not.
To get an even number, both m and n must be either odd or even.

Statement 1: m>10
Prime numbers greater than 10 is always odd. By plugging in numbers....
If m=11 and n=13, \(m^2 + n^2\) is even.....yes
But, if m=11 and n=2, \(m^2 + n^2\) is odd.....no
Different answers. Insufficient.

Statement 2: n>20
Prime numbers greater than 20 is always odd. By plugging in numbers....
If m=11 and n=23, \(m^2 + n^2\) is even.....yes
But, if m=2 and n=23, \(m^2 + n^2\) is odd.....no
Different answers. Insufficient.

Combined 1 & 2: m>10 & n>20
All prime numbers in this range is odd. So, \((odd)^2\)+\((odd)^2\) will ALWAYS be even. Hence, sufficient.
IMO answer is option C.

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If n is an integer, is (n+1)(n+2)(n+3) divisible by 12?

1) n is an even number.
2) n is a multiple of 4.

Answer: B

#1
for n = 2 ; we get yes sufficient
n=4 . we get not sufficient

#2
n=4,8,12
for all such values of n . the expression is not divisible by 12
sufficinet
IMO B

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n is a positive integer. What is the remainder when n is divided by 3?

1) n^2 has remainder 1 when it is divided by 3
2) n has remainder 7 when it is divided by 9

#1
n=2,5,8 we get remainder as 2 when divided by 3
and n=4,7. we get remainder as 1 when divided by 3
in sufficient
#2
n= 11,34
remainder as 1
sufficient
IMO B

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Is x = y?

1) x ≤ y
2) |x| ≥ |y|

Answer: E

#1
y=1, x=1 yes sufficeint
y=2 ,x=1, in sufficient
#2
x & y can be of same or opposite signs
in sufficient
IMO E

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[GMAT math practice question]

(number properties) If \(m\) and \(n\) are prime numbers, is \(m^2 + n^2\) an even number?

\(1) m > 10\)
\(2) n > 20\)

#1
m=11,13,17..
n=2,3,5,7,11..
so m^2+n^2 = even and odd both as n value not given
in sufficeint
#2
same as #1 value of m not sure . in sufficient as at m=2 eqn would be odd and else even

from 1 & 2
m>10 and n>20
we have odd integers so addition of odd + odd= even ; sufficient
IMO C

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Updated on: 08 Nov 2021, 02:11

Originally posted by MathRevolution on 03 Mar 2019, 18:31.
Last edited by MathRevolution on 08 Nov 2021, 02:11, edited 1 time in total.

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Is x = y?

1) x ≤ y
2) |x| ≥ |y|

Answer: E

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Updated on: 30 Dec 2021, 01:16

Originally posted by MathRevolution on 03 Mar 2019, 18:34.
Last edited by MathRevolution on 30 Dec 2021, 01:16, edited 1 time in total.

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[GMAT math practice question]

(number properties) If \(m\) and \(n\) are prime numbers, is \(m^2 + n^2\) an even number?

\(1) m > 10\)
\(2) n > 20\)

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

In order for \(m^2 + n^2\) to be even, either both \(m\) and \(n\) must be even or both \(m\) and \(n\) must be odd. Since \(m\) and \(n\) are primes, we must have both \(m\) and \(n\) odd numbers as they are both greater than \(10\). Thus, C is the answer.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If \(m = 11\) and \(n = 3\), then \(m^2+n^2 = 11^2+3^2 = 121 + 9 = 130\) is an even number, and the answer is “yes”.
If \(m = 11\) and \(n = 2\), then \(m^2+n^2 = 11^2+2^2 = 121 + 4 = 125\) is an odd number, and the answer is “no”.
Thus, condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
If \(m = 3\) and \(n = 23\), then \(m^2+n^2 = 3^2+23^2 = 9 + 529 = 538\) is an even number, and the answer is “yes”.
If \(m = 2\) and \(n = 23\), then \(m^2+n^2 = 2^2+23^2 = 4 + 529 = 533\) is an odd number, and the answer is “no”.
Thus, condition 2) is not sufficient since it does not yield a unique solution.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

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[GMAT math practice question]

(number properties) \(k\) is a positive integer. When \(2^{\frac{-k}{2}} ≤ \frac{1}{1},024, k=?\)

1) \(k\) is an integer less than \(21\)
2) \(k\) is an integer greater than \(12\)

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[GMAT math practice question]

(number properties) When \(32\) is divided by \(k\), the remainder is \(k-3\). What is the value of \(k\)?

\(1) k>20\)
\(2) k<40\)

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[Math Revolution GMAT math practice question]

(number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)?

1) \(n\) is a prime number
2) \(\frac{(n+2)}{n}\) is an integer

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.
If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer.
If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer.
If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer.
Thus \(n = 2\) is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

The answer should B as it is already mentioned in the question that n is greater than 1 (n>1)

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Updated on: 14 Jan 2022, 04:03

Originally posted by MathRevolution on 06 Mar 2019, 01:59.
Last edited by MathRevolution on 14 Jan 2022, 04:03, edited 1 time in total.

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[GMAT math practice question]

(geometry) Is a triangle, with one side of length \(12\), inscribed in a circle a right triangle?

1) The area of the circle is \(36π\).
2) The circumference of the circle is \(12π\).

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Updated on: 14 Jan 2022, 04:03

Originally posted by MathRevolution on 07 Mar 2019, 01:13.
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[GMAT math practice question]

(number properties) When \(32\) is divided by \(k\), the remainder is \(k-3\). What is the value of \(k\)?

\(1) k>20\)
\(2) k<40\)

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[GMAT math practice question]

(statistics) Is the average (arithmetic mean) of \(x, y,\) and \(z\) equal to their median?

1) \(y\) is the average (arithmetic mean) of \(x, y,\) and \(z\)
2) \(z = 2y - x\)

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Attachment:

3.8.png [ 7.42 KiB | Viewed 1529 times ]

If a side of a triangle is the diameter of its circumscribed circle, then the triangle is a right triangle.

Condition 1)
A circle with area \(36π\) has radius \(6\) and diameter \(12\). So, the answer is ‘yes’ and condition 1) is sufficient.

Condition 2)
A circle with circumference \(12π\) has diameter \(12\). So, the answer is ‘yes’ and condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Note that if conditions 1) and 2) yield the same information, Tip 1 of the VA method tells us that D is most likely to be the answer.