GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #3 : Absolute Value

Is $\left | a-b \right |<\left | a-c \right |?$

(1) a>0

(2) $\left | b \right |<\left | c \right |$

Possible Answers:

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

Statements (1) and (2) TOGETHER are NOT sufficient.

EACH statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Correct answer:

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

For statement (1), since we don’t know the value of and , we have no idea about the value of $\left | a-b \right |$ and $\left | a-c \right |$ .

For statement (2), since we don’t know the sign of and , we cannot compare $\left | a-b \right |$ and $\left | a-c \right |$ .

Putting the two statements together, if a-b>0 and a-c>0 , then $\left | a-b \right |<\left | a-c \right |$ .

But if a-b<0 and a-c<0 , then $\left | a-b \right |>\left | a-c \right |$ .

Therefore, we cannot get the only correct answer for the questions, suggesting that the two statements together are not sufficient. For this problem, we can also plug in actual numbers to check the answer.

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Example Question #4 : Absolute Value

Is nonzero number positive or negative?

Statement 1: N + |N| = 0

Statement 2: $N^{2} + 5N < 0$

Possible Answers:

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.

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

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If we assume that N + |N| = 0 , then it follows that:

N + |N| - |N| = 0- |N|

N = - |N|

Since we know $N \neq 0$ , we know |N| is positive, and - |N| and are negative.

If we assume that $N^{2} + 5N < 0$ , then it follows that:

$N^{2} + 5N -N^{2} < 0-N^{2}$

$5N < -N^{2}$

$N < -\frac{N^{2}}{5}$

Since we know $N \neq 0$ , we know $N^{2}$ is positive. $\frac{N^{2}}{5}$ is also positive and $-\frac{N^{2}}{5}$ is negative; since is less than a negative number, is also negative.

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Example Question #5 : Absolute Value

True or false: N < 7

Statement 1: $\left | N\right | <7$

Statement 2: $N^{2} < 49$

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT 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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 and Statement 2 are actually equivalent.

If $\left | N\right | <7$ , then either -7 < N < 7 by definition.

If $N^{2} < 49$ , then either -7 < N < 7 .

From either statement alone, it can be deduced that N < 7 .

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Example Question #6 : Absolute Value

is a real number. True or false: N > 10

Statement 1: $\left | N\right | > 10$

Statement 2: $N^{2} > 100$

Possible Answers:

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.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Statement 1 and Statement 2 are actually equivalent.

If $\left | N\right | > 10$ , then either N > 10 or N < -10 by definition.

If $N^{2} > 100$ , then either N > 10 or N < -10 .

The correct answer is that the two statements together are not enough to answer the question.

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Example Question #6 : Absolute Value

is a real number. True or false: $\left | N\right | < 5$

Statement 1: $\left | N - 1\right | < 4$

Statement 2: $\left | N +1 \right | <6$

Possible Answers:

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.

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:

If $\left | N\right | < 5$ , then, by definition, -5 < N < 5 .

If Statement 1 is true, then

$\left | N - 1\right | < 4$

-4 < N - 1 < 4

-3 < N < 5 ,

so must be in the desired range.

If Statement 2 is true, then

$\left | N +1 \right | <6$

-6 < N +1 <6

-7< N <5

and is not necessarily in the desired range.

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Example Question #7 : Absolute Value

is a real number. True or false: N > 5

Statement 1: $\left | N\right | > 5$

Statement 2: $N^{3} > 125$

Possible Answers:

BOTH statements TOGETHER are insufficient 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.

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

Correct answer:

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

Explanation:

If $\left | N\right | > 5$ , then we can deduce only that either N > 5 or N < -5 . Statement 1 alone does not answer the question.

If $N^{3} > 125$ , then must be positive, as no negative number can have a positive cube. The positive numbers whose cubes are greater than 125 are those greater than 5. Therefore, Statement 2 alone proves that N > 5 .

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Example Question #4 : Dsq: Understanding Absolute Value

is a real number. True or false: $\left | N\right | < 6$

Statement 1: $N^{2} > 36$

Statement 2: $N^{3} > 216$

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 insufficient to answer the question.

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.

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

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If $\left | N\right | < 6$ , then, by definition, -6 < N < 6 .

If Statement 1 holds, that is, if $N^{2} > 36$ , one of two things happens:

If is positive, then $N > \sqrt{36} = 6$ .

If is negative, then $N < - \sqrt{36} = -6$ .

$\left | N\right | < 6$ is a false statement.

If Statement 2 holds, that is, if $N^{3} > 216$ , we know that is positive, and

$N >\sqrt[3]{ 216} = 6$

$\left | N\right | < 6$ is a false statement.

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Example Question #7 : Dsq: Understanding Absolute Value

is a real number. True or false: $\left | N \right | < 5$

Statement 1: 2 N + 7 < 17

Statement 2: 4N - 17 > -37

Possible Answers:

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.

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:

If $\left | N\right | < 5$ , then, by definition, -5 < N < 5 - that is, both N < 5 and N > -5 .

If Statement 1 is true, then

2 N + 7 < 17

2 N < 10

N < 5

Statement 1 alone does not answer the question, as N < 5 follows, but not necessarily N > -5 .

If Statement 2 is true, then

4N - 17 > -37

4N >-20

N > -5

Statement 2 alone does not answer the question, as N > -5 follows, but not necessarily N < 5 .

If both statements are true, then N > -5 and N < 5 both follow, and -5 < N < 5 , meaning that $\left | N \right | < 5$ .

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Example Question #11 : Dsq: Understanding Absolute Value

Of distinct integers a, b, c , which is the greatest of the three?

Statement 1: |b| <a < |c|

Statement 2: |a | + |b| = |c|

Possible Answers:

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.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The two statements together are insufficient.

For example, let a = 8, b=6 . Then, from Statement 2,

|c| = |a| + |b| = |6 | + |8| = 6 + 8 = 14

Therefore, either c = - 14 or c = 14 .

In either case, Statement 2 is shown to be true, since

6 < 8 < 14

and

|b| <a < |c|

But if c = - 14 , then is the greatest of the three. If c = 14 , then is the greatest. Therefore,the two statements together are not enough.

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Example Question #11 : Dsq: Understanding Absolute Value

Of distinct integers a, b, c , which is the greatest of the three?

Statement 1: |a| < b < |c|

Statement 2: and are negative.

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.

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.

Correct answer:

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

Explanation:

Statement 1 alone gives insufficient information.

Case 1: a=4 , b= 5, c =6

|a|< b < |c|

|4|< 5 < |6|

4< 5 < 6 , which is true.

Case 2: a=-4 , b= 5, c =-6

|a|< b < |c|

|-4|< 5 < |-6|

4< 5 < 6 , which is true.

But in the first case, is the greatest of the three. In the second, is the greatest.

Statement 2 gives insuffcient information, since no information is given about the sign of .

Assume both statements to be true. $|a| \ge 0$ , and from Statement 1, b > |a| ; by transitivity, b > 0 . From Statement 2, a < 0, c < 0 . This makes the greatest of the three.

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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 #3 : Absolute Value

Example Question #4 : Absolute Value

Example Question #5 : Absolute Value

Example Question #6 : Absolute Value

Example Question #6 : Absolute Value

Example Question #7 : Absolute Value

Example Question #4 : Dsq: Understanding Absolute Value

Example Question #7 : Dsq: Understanding Absolute Value

Example Question #11 : Dsq: Understanding Absolute Value

Example Question #11 : Dsq: Understanding Absolute Value

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