GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #1 : Dsq: Understanding The Properties Of Integers

If and are both integers, evaluate x+y .

Statement 1: 13 < x < y < 23 .

Statement 2: and are both prime integers.

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 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.

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:

There are infinitely many primes, and several integers between 13 and 23, so knowing just one of these statements is not enough. But only two integers in the stated range - 17 and 19 - are prime, so knowing both statements tells you that and are 17 and 19, respectively. Subsequently, you can add them to get 36.

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Example Question #2 : Dsq: Understanding The Properties Of Integers

If a positive integer is divided by 2, what is the remainder?

Statement 1: If $N^{2 }$ is divided by 2, the remainder is 1.

Statement 2: If is divided by 4, the remainder is 3.

Possible Answers:

BOTH statements TOGETHER are insufficient 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 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:

The question is the same as asking whether is odd or even.

Statement 1 says that the square of is odd. If we know this, then we know that is odd, since the square of an even number is even.

Statement 2 says that is 3 greater than a multiple of 4; this makes odd.

Therefore, either statement alone tells us that is an odd number.

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Example Question #5 : Arithmetic

What is the last digit of a positive integer ?

Statement 1: The last digit of $N^{2}$ is 1.

Statement 2: The last digit of $N^{3}$ is 1.

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:

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

Explanation:

If the last digit of $N^{2}$ is 1, then the last digit of is either 1 or 9.

If the last digit of $N^{3}$ is 1, however, the last digit of must be 1.

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Example Question #11 : Dsq: Understanding The Properties Of Integers

How many negative numbers are in the set $\left \{ A,B,C,D,E,F\right \}$ ?

Statement 1: AB < 0, CD < 0, EF < 0

Statement 2: ABC > 0, DEF < 0

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.

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.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 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:

Statement 1 tells you that and are of unlike sign, that and are of unlike sign, and that and are of unlike sign; that is, exactly one number from each pair is negative. Therefore, there are three negative numbers.

Statement 2 tells you that of , , and , there can be either exactly zero or two negative numbers; and that of , , and , there can be exactly one or three negative numbers. This means that the number of negative numbers among the six can be as few as one or as many as five.

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Example Question #12 : Dsq: Understanding The Properties Of Integers

This six-digit number has two digits missing:

456 ______

If the blanks are to be filled with the same digit, what is that digit?

Statement 1: The number is divisible by 4.

Statement 2: The number is divisible by 3.

Possible Answers:

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.

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:

If the number is divisible by 4, then the last two digits make a number that is divisible by 4; this allows that digit to be 0, 4, or 8.

If the number is divisible by 3, then its digit sum is divisible by 3. This allows the comon digit to be 1, 4, or 7:

4+5+6+1+4+1 = 21

4+5+6+4+4+4 = 27

4+5+6+7+4+7 = 33

Neither statement alone narrows the common digit to one possibility, but if both statements are true, the only possibility becomes 4.

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Example Question #13 : Dsq: Understanding The Properties Of Integers

This five-digit number has two digits missing:

______

If both blanks are two be filled with the same digit, what is that digit?

Statement 1: The number is divisible by 5.

Statement 2: The number is not divisible by 3.

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.

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.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

There are two different choices we can make for the common digit that would make both statements true, 0 and 5. This makes the last digit 0 or 5, making Statement 1 true, Also, this makes the digit sum either

8+5+0+6+0 = 19

8+5+5+6+5 = 29

Either way, the digit sum is not a multiple of 3, and the number itself is not a multiple of 3.

Therefore, the two statements together do not provide enought information to answer the question definitively.

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Example Question #3101 : Gmat Quantitative Reasoning

You are given four numbers, A,B,C,D . You know that exactly one of these numbers does not have value 0. Which number is it?

Statement 1: AB=0

Statement 2: CD=0

Possible Answers:

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.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Neither of these statements help you, individually or together. If three of the four numbers are equal to zero, then both products will equal zero. There is no way of knowing which of the numbers is non-zero.

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Example Question #15 : Dsq: Understanding The Properties Of Integers

Let M,N be positive integers. When is $M^{2} + 4 N^{2}$ an odd number?

Possible Answers:

$M^{2} + 4 N^{2}$ is odd if and only if exactly one of M,N is odd.

$M^{2} + 4 N^{2}$ is never odd.

$M^{2} + 4 N^{2}$ is always odd.

$M^{2} + 4 N^{2}$ is odd if and only if both of M,N are odd.

$M^{2} + 4 N^{2}$ is odd if and only if is odd.

Correct answer:

$M^{2} + 4 N^{2}$ is odd if and only if is odd.

Explanation:

The square of an integer assumes the same parity (even or odd) as the integer itself, so $M^{2}$ is odd if and only if is odd. $4N^{2}$ is always even, having even factor 4. The sum of any integer and an even integer has the same parity as the first integer. Therefore, $M^{2} + 4 N^{2}$ assumes the same parity as $M^{2}$ , and, subsequently, the same parity as . In other words, $M^{2} + 4 N^{2}$ is odd if and only if is odd.

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Example Question #13 : Dsq: Understanding The Properties Of Integers

You are given four numbers, A,B,C,D . How many of these numbers have value 0?

Statement 1: AB = 0,CD>0

Statement 2: ACD < 0

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.

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.

Correct answer:

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

Explanation:

The product of two or more numbers is 0 if and only if at least one of the factors is 0.

If you know the first statement, you know that neither nor is equal to 0, and that either A,B , or both are equal to 0. You have narrowed the answer down to one or two.

If you know the second statement, you know that A,C, and are nonzero, but you know nothing about . You have narrowed the answer down to none or one.

If you know both statements, though, you know that is the only one of the four numbers equal to zero, so you have answered the question.

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Example Question #14 : Dsq: Understanding The Properties Of Integers

What is the last digit in the base eight representation of a number?

Statement 1: The number divided by 8 yields a remainder of 5.

Statement 2: The number divided by 16 yields a remainder of 13.

Possible Answers:

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.

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

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

To find the last digit in the base representation of a number, divide the number by ; the remainder is that digit. If we know the number divided by 8 has remainder 5, we know its last base-eight digit is 5. If we know the number divided by 16 is 13, then we still know that the digit is 5, since the reminder when divided by 8 would be 13-8=5 .

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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 #1 : Dsq: Understanding The Properties Of Integers

Example Question #2 : Dsq: Understanding The Properties Of Integers

Example Question #5 : Arithmetic

Example Question #11 : Dsq: Understanding The Properties Of Integers

Example Question #12 : Dsq: Understanding The Properties Of Integers

Example Question #13 : Dsq: Understanding The Properties Of Integers

Example Question #3101 : Gmat Quantitative Reasoning

Example Question #15 : Dsq: Understanding The Properties Of Integers

Example Question #13 : Dsq: Understanding The Properties Of Integers

Example Question #14 : Dsq: Understanding The Properties Of Integers

All GMAT Math Resources

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