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 two consecutive integers are always relatively prime, the greatest common divisor of m and n is 1. Thus, condition 1) is sufficient. Condition 2) If m = 2 and n = 3 , then the greatest common divisor of m and n is 1 . If m = 2 and n = 4, then the greatest common divisor of m and n is 2 . Thus, condition 2) is not sufficient since it does not yield a unique solution. Therefore, the correct answer is A. Answer: A

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MathRevolution

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[Math Revolution GMAT math practice question]

(number properties) If $n$ is a positive integer, is $\sqrt{17n}$ an integer?

1) $68n$ is the square of an integer.
2) $\frac{n}{68}$ is the square of an integer.

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Updated on: 19 Aug 2021, 02:39

Originally posted by MathRevolution on 29 Nov 2018, 02:44.
Last edited by MathRevolution on 19 Aug 2021, 02:39, edited 1 time in total.

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[Math Revolution GMAT math practice question]

(functions) In the x-y plane, line l passes through points $(-1,-1)$ and $(3,k)$. What is the value of $k$?

1) The y-intercept of line l is $1$
2) The slope of line l is $2$

=>

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 ($k$) and $0$ equations in the original condition, D is most likely to be the answer. So, we should consider each condition on its own first.

We consider the equation of the line $l, y = mx + b.$ Since it passes through the points $(-1,-1)$ and $(3,k),$ we can plug these points into its equation to yield $-1 = -m + b$ and $k = 3m + b.$

Since we have $3$ variables and $2$ equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since the y-intercept of line $l$ is $1$, we have $b = 1$ and $m = b + 1 = 2.$
Thus, $k = 3m + b = 3*2 + 1 = 7.$
Condition 1) is sufficient.

Condition 2)
Since the slope of line $l$ is $2$, we have $m = 2$ and $b = m – 1 = 1.$
Thus, $k = 3m + b = 3*2 + 1 = 7.$
Condition 2) is sufficient.

Answer: D

Note: When we checked the two conditions, we showed that both were equivalent in terms of b. So, each condition is sufficient by Tip 1)
of the VA method, which states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

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.

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29 Nov 2018, 02:45

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[Math Revolution GMAT math practice question]

(integer) If $m$ and $n$ are positive integers, what is the greatest common divisor of $m$ and $n$?

$1) m=n+1$
$2) m*n$ is divisible by $2$

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Updated on: 19 Aug 2021, 02:42

Originally posted by MathRevolution on 30 Nov 2018, 01:56.
Last edited by MathRevolution on 19 Aug 2021, 02:42, edited 1 time in total.

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=>

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.

Modifying the question:
The question asks if $\sqrt{17n} = a$ for some integer a. This is equivalent to asking if $17n = a^2$ for some integer a.

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 $68n$ is the square of an integer and $68 = 4*17$, we must have $68n = 4*17*17*k^2$ for some integer $k$, and $n = 17*k^2$ or $17n = 17^2*k^2 = (17*k)^2.$
Thus, $17n$ is the square of the integer $17k$, and condition 1) is sufficient.

Condition 2)
Since $\frac{n}{68}$ is a square of an integer and $68 = 4*17$, we have $\frac{n}{68} = m^2$ for some integer $m$, and $n = 17*4*m^2$ or $17n = 17^2*2^2*m^2 = (34m)^2.$
Thus, $17n$ is the square of the integer $17k$, and condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

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.

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[Math Revolution GMAT math practice question]

(number property) If $k$ is a positive integer and $n=(k-1)k(k+1)$, is $n$ a multiple of $8$?

1) $k$ is an odd number
2) $k = 1$

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30 Nov 2018, 08:45

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[Math Revolution GMAT math practice question]

(number property) If $k$ is a positive integer and $n=(k-1)k(k+1)$, is $n$ a multiple of $8$?

1) $k$ is an odd number
2) $k = 1$

From statement 1:

k is an odd number.
Let k be 2k+1
Then n = (2k+1-1)(2k+1)(2k+2)
n = 8k^3+12k^2+4k.
For an odd value of k. n will always be a multiple of 8.
Sufficient.

From statement 2:
k = 1.
n = 0. 0 is a multiple of 8.
Sufficient.

D is the answer.

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Updated on: 11 Sep 2021, 03:06

Originally posted by MathRevolution on 02 Dec 2018, 18:50.
Last edited by MathRevolution on 11 Sep 2021, 03:06, edited 1 time in total.

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[Math Revolution GMAT math practice question]

(number property) If $k$ is a positive integer and $n=(k-1)k(k+1)$, is $n$ a multiple of $8$?

1) $k$ is an odd number
2) $k = 1$

=>

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 $2$ variables ($n$ and $k$) and $1$ equation, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since $k$ is an odd number, $k – 1$ and $k + 1$ are consecutive even integers.
Any product of consecutive even integers is a multiple of $8$.
Thus, condition 1) is sufficient.

Condition 2)
Since $k = 1$, we have $n = (k-1)k(k+1) = 0*1*2 = 0. 0$ is a multiple of any number, so $n = 0$ is a multiple of $8$.
Thus, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Since this question is a CMT4(B) question. Condition 2) is easy to understand and condition 1) is hard. When one condition is easy to understand, and the other is hard, D is most likely to be the answer.

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.

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02 Dec 2018, 23:51

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[Math Revolution GMAT math practice question]

(inequality) Is $x + \frac{1}{x} > 2$?

$1) x > 0$
$2) x ≠ 1$

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03 Dec 2018, 00:54

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[Math Revolution GMAT math practice question]

(inequality) Is $x + \frac{1}{x} > 2$?

$1) x > 0$
$2) x ≠ 1$

From statement 1:

x>0. If x = 1. then x+1/x = 2. And 2 is not greater than 2.
If x = 2. Then x+1/x = 2.5>2. hence insufficiennt.

From statement 2:

x not equal to 1.
If x = -1. Then x+1/x = -2, which is not greater than 2.
If x = 2. Then x+1/x = 2.5>2. hence insufficient.

Combining both tell that x>0 and x not equal to 0. Then x+1/x is always greater than 2.
C is the answer.

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MathRevolution

[Math Revolution GMAT math practice question]

(inequality) Is $x + \frac{1}{x} > 2$?

$1) x > 0$
$2) x ≠ 1$

Excellent problem, Max. Congrats! (kudos!)

$x + {1 \over x}\,\,\mathop > \limits^? \,\,2$

$\left( 1 \right)\,\,x > 0\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$

$\left( 2 \right)\,\,x \ne 1\,\,\left\{ \matrix{\\
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,x = - 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.$

$\left( {1 + 2} \right)\,\,\,0\,\,\mathop < \limits^{x\, \ne \,1} \,\,{\left( {x - 1} \right)^2}\,\, = \,\,\,{x^2} - 2x + 1\,\,\,\,\mathop \Leftrightarrow \limits^{\,x\, > \,\,0} \,\,\,\,0 < {{{x^2} - 2x + 1} \over x} = x - 2 + {1 \over x}\,\,\,\,\, \Leftrightarrow \,\,\,\,x + {1 \over x} > 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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[Math Revolution GMAT math practice question]

(number properties) $n$ is a positive integer. Is $n$ divisible by $3$?

1) $\frac{36}{n}$ is divisible by $3$
2) $\frac{27}{n}$ is divisible by $3$

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[Math Revolution GMAT math practice question]

(inequality) Is $x + \frac{1}{x} > 2$?

$1) x > 0$
$2) x ≠ 1$

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[Math Revolution GMAT math practice question]

(statistics) $x$ is a positive number. What is the median of $x, √x$ and $x^2$?

$1) x^2=x$
$2) x^2+x+1=3x$

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06 Dec 2018, 00:28

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=>

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 in the original condition, D is most likely to be the answer. So, we should consider each condition on its own first. It is suggested we plug in numbers when solving remainder problems.

Condition 1)
If $n = 3$, then $\frac{36}{3} = 12$ is divisible by $3$, and $n$ is divisible by $3$. The answer is ‘yes’.
If $n = 1$, then $\frac{36}{1} = 36$ is divisible by $3$, but $n$ is not divisible by $3$. The answer is ‘no’.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
If $n = 3$, then $\frac{27}{3} = 9$ and $n$ is divisible by $3$. The answer is ‘yes’.
If $n = 1$, then $\frac{27}{1} = 27$ and $n$ is not divisible by $3$. The answer is ‘no’.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Conditions 1) & 2)
Even if we consider both conditions together, we still have two possible values of $n: n = 1$ and $3$.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

Therefore, E is the answer.
Answer: E

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.

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06 Dec 2018, 00:29

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[Math Revolution GMAT math practice question]

(number properties) If $a$ and $b$ are integers, is $a-b$ an even number?

1) $a^2b^2$ is an even number
2) $a^2+2b^2$ is an even number

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07 Dec 2018, 00:57

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[Math Revolution GMAT math practice question]

(statistics) $x$ is a positive number. What is the median of $x, √x$ and $x^2$?

$1) x^2=x$
$2) x^2+x+1=3x$

=>

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.

If $x >1$, then $√x < x < x^2$ and $x$ is their median.
If $0 < x <1$, then $√x > x > x^2$ and $x$ is their median.
If $x = 1$, then $√x = x = x^2$ and $x$ is their median.
Thus, the question asks for the value of $x$.

Since we have $1$ variable ($x$) and $0$ equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
$x^2=x$
$=> x^2-x=0$
$=> x(x-1)=0$
$=> x = 0$ or $x = 1$
Since $x$ is positive, $x = 1.$
Condition 1) is sufficient.

Condition 2)
$x^2+x+1=3x$
$=> x^2-2x+1=0$
$=> (x-1)^2=0$
$=> x = 1$.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

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.

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07 Dec 2018, 00:58

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[Math Revolution GMAT math practice question]

(inequality) Is $x>y$?

$1) x+y>2$
$2) x^2<2y$

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08 Dec 2018, 18:00

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(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

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09 Dec 2018, 18:59

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[Math Revolution GMAT math practice question]

(number properties) If $a$ and $b$ are integers, is $a-b$ an even number?

1) $a^2b^2$ is an even number
2) $a^2+2b^2$ is an even number

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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.

Modifying the question:
For $a – b$ to be an even number, either both a and b must be even numbers or both a and b must be odd numbers.

Since we have $2$ variables ($a$ and $b$) and $0$ equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
From condition 2), a is an even number.
From condition 1), b might either be even or odd.

Thus, both conditions together are not sufficient, since they do not yield a unique solution.

Therefore, the correct answer is E.
Answer: E

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.