GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #4 : Dsq: Solving Equations

Solve for $x,y,and\ z.$

Statement 1: 5x-3y+2z=1

Statement 2: 2y-5z=2,z=2

Possible Answers:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

EACH statement ALONE is sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

Correct answer:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

To solve for three unknowns, we need three equations. Here we have three equations if we use both statements 1 and 2. We don't need to solve any further. Because this is a data sufficiency question, it doesn't matter what the actual values of x, y, and z are. The important fact is the we could find them if we wanted to.

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Example Question #7 : Dsq: Solving Equations

The volume of a fixed mass of gas varies inversely with the atmospheric pressure, in millibars, acting upon it, given that all other conditions remain constant.

At 12:00, a balloon was filled with exactly 100 cubic yards of helium. What is its current volume?

Statement 1: It is now 2:00.

Statement 2: The atmospheric pressure is now 105 millibars.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The first statement is unhelpful; the time of day is irrelevant to the question.

You can use the following variation equation to deduce the current volume:

$V_{1} P _{1} = V_{2} P _{2}$

or, equivalently,

$V_{2} = \frac{V_{1} P _{1} }{P _{2}}$

To find the current volume $V_{2}$ , you therefore need three things - the initial volume $V_{1}$ , which is given in the body of the question; the current pressure $P_{2}$ , which you know if you use Statement 2, and the initial pressure $P_{1}$ , which is not given anywhere.

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Example Question #8 : Dsq: Solving Equations

The electrical current through an object in amperes varies inversely as the object's resistance in ohms, given that all other conditions are equal.

Four batteries hooked up together run an electrical current of 3.2 amperes through John's flashlight. How much current would the same batteries run through John's radio?

Statement 1: The radio has resistance 20 ohms.

Statement 2: The flashlight has resistance 15 ohms.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Let $I_{1},R_{1}$ be the current through and the resistance of the flashlight; let $I_{2},R_{2}$ be the current through and the resistance of the radio.

The variation equation here would be:

$\frac{I_{1}}{R_{1}} = \frac{I_{2}}{R_{2}}$

or equivalently:

$\frac{I_{1}}{R_{1}} \cdot R_{2}= \frac{I_{2}}{R_{2}} \cdot R_{2}$

$I_{2} = \frac{I_{1}R_{2}}{R_{1}}$

So in order to find the current in the radio, you need to know three things - the current $I_{1}$ in the flashlight, which you know from the body of the problem; the resistance from the flashlight $R_{1}$ , which you know if you are given Statement 2; and the resistance from the radio $R_{2}$ , which you know if you are given Statement 1. Just substitute and solve.

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Example Question #9 : Dsq: Solving Equations

Evaluate:

$\log_{x} 100y - \log_{x} y$

Statement 1: x =10

Statement 2: y = 4

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

The difference of two logarithms with the same base is the same-base logarithm of the quotient of the numbers. Therefore, we can simplify this expression as

$\log_{x} 100y - \log_{x} y =\log_{x} \frac{100y}{y} = \log_{x} 100$

We need only know the value of , given to us in Statement 1, in order to evaluate this expression.

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Example Question #3 : Dsq: Solving Equations

is a positive integer

True or false?

(x - 2)(x-4)(x-6) = 0

Statement 1: x < 8

Statement 2: is even.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

By the zero product principle, we can solve by setting each linear binomial to zero and solving. This yields three solutions:

$y - 2 = 0 \Rightarrow y = 2$

$y - 4 = 0 \Rightarrow y =4$

$y - 6= 0 \Rightarrow y = 6$

Neither statement alone narrows to one of these three solutions, but the two together do.

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Example Question #3051 : Gmat Quantitative Reasoning

Solve for :

$\left | 4x-3\right |-17=y^{2}-z^{2}$

(1) y-z=4

(2) y+z=12

Possible Answers:

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Each statement ALONE is sufficient

Both statements TOGETHER are not sufficient

Correct answer:

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Explanation:

Solution

To solve for x, we need the value of $y^{2}-z^{2}$

$y^{2}-z^{2}=(y-z)(y+z)$

Therefore, we need both statements in order to solve for x.

$\left | 4x-3\right |-17= 4\times12$

$\left | 4x-3\right |-17=48$

$\left | 4x-3\right |=65$

4x-3=65 Or

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Example Question #11 : Equations

is a number not in the set $\left\{-1, 0, 1 \right\}$ .

Of the elements $\left \{ x, x^{2}, x^{3}\right \}$ , which is the greatest?

Statement 1: is a negative number.

Statement 2: $\left | x\right |>1$

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. If is a negative number, then of the three given powers of in the set, only $x^{2}$ (the only even power) is positive. This makes $x^{2}$ the greatest of the three, thereby giving an answer to the question.

We show that Statement 2 alone is inconclusive by examining two values of whose absolute values are greater than 1 - namely, $\left \{-2, 2 \right \}$ .

Case 1: x = 2 . Then $x^{2}= 4$ and $x^{3} = 8$ , making $x^{3}$ the greatest number of the three.

Case 2: x = -2 . Then $x^{2}= 4$ and $x^{3} = -8$ , making $x^{2}$ the greatest number of the three.

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Example Question #11 : Dsq: Solving Equations

The volume of a fixed mass of gas varies inversely with the atmospheric pressure, in millibars, acting upon it, given that all other conditions remain constant.

At 12:00, a balloon was filled with exactly 100 cubic yards of helium. What its current volume?

Statement 1: The atmospheric pressure at 12:00 was 109 millibars.

Statement 2: The atmospheric pressure is now 105 millibars.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

You can use the following variation equation to deduce the current volume:

$V_{1} P _{1} = V_{2} P _{2}$

or, equivalently,

$V_{2} = \frac{V_{1} P _{1} }{P _{2}}$

To find the current volume $V_{2}$ , you therefore need three things - the initial volume $V_{1}$ , which is given in the body of the question; the initial pressure $P _{1}$ , which you know if you are given Statement 1; and the current pressure, $P _{2}$ , which you know if you are given Statement 2. Just substitute, and solve.

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Example Question #14 : Dsq: Solving Equations

is a rational number. True or false: N = 7

Statement 1: $N^{2} + 4N + 100 = 18N + 51$

Statement 2: |N - 14| = N

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

Assume Statement 1 alone.

$N^{2} + 4N + 100 = 18N + 51$

$N^{2} + 4N + 100- 18 N - 51 = 18N + 51 - 18 N - 51$

$N^{2} -14N +49 =0$

$(N-7)^{2} = 0$

N-7 = 0

N= 7

Assume Statement 2 alone. If |N - 14| = N , then either N - 14 = N or N - 14 =- N , so we can examine both scenarios.

Case 1:

N - 14 = N

N - 14- N = N - N

-14 = 0

This is identically false, so we dismiss this case.

Case 2:

N - 14 =- N

N - 14 + N + 14 =- N + N + 14

2N = 14

N = 7

Since each equation has only 7 as a solution, either statement alone is sufficient to identify N = 7 as a true statement.

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Example Question #14 : Dsq: Solving Equations

is a real number. True or false: is positive.

Statement 1: $3^{N} > \frac{1}{3}$

Statement 2: The arithmetic mean of 100 and is positive.

Possible Answers:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

Explanation:

Assume both statements are true. We show that we cannot determine for certain whether or not is positive.

Case 1: N = 0

$3^{N} = 3^{0} = 1 > \frac{1}{3}$ , satisfying the condition of Statement 1.

The arithmetic mean of 0 and 100 is half their sum, which is $\frac{0+100}{2} = 50$ , a positive number; the condition of Statement 2 is satisfied.

Case 2: N = 2

$3^{N} = 3^{2} = 9 > \frac{1}{3}$ , satisfying the condition of Statement 1.

The arithmetic mean of 2 and 100 is half their sum, which is $\frac{2+100}{2} = 51$ , a positive number; the condition of Statement 2 is satisfied.

Therefore, may or may not be positive.

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GMAT Math : Data-Sufficiency Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #4 : Dsq: Solving Equations

Example Question #7 : Dsq: Solving Equations

Example Question #8 : Dsq: Solving Equations

Example Question #9 : Dsq: Solving Equations

Example Question #3 : Dsq: Solving Equations

Example Question #3051 : Gmat Quantitative Reasoning

Example Question #11 : Equations

Example Question #11 : Dsq: Solving Equations

Example Question #14 : Dsq: Solving Equations

Example Question #14 : Dsq: Solving Equations

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