GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #2 : Integers And Types Of Numbers

If a and b are even integers, what must be odd?

Possible Answers:

$\dpi{100} \small a-b$

$\dpi{100} \small a\times b$

$\dpi{100} \small a+b-2$

$\dpi{100} \small a+b-1$

$\dpi{100} \small a+b$

Correct answer:

$\dpi{100} \small a+b-1$

Explanation:

The sum (or difference) or 2 even integers is even. Similarly, the product (or quotient) of 2 even integers is also even; therefore the answer must be $\dpi{100} \small a+b-1$ , which can be easily checked by plugging in any two even numbers.

For example, if $\dpi{100} \small a=2\ and\ b=4,\ a+b-1=2+4-1=5$ , which is odd.

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Example Question #2 : Properties Of Integers

Three consecutive numbers add up to 36. What is the smallest number?

Possible Answers:

Correct answer:

Explanation:

The sum of 3 consecutive numbers would be

n + (n +1) + (n+2)

which simplifies into

3n +3

Set that equation equal to 36 and solve.

$3n + 3 = 36 \rightarrow 3n = 33 \rightarrow n = 11$

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Example Question #1721 : Problem Solving Questions

Becky has to choose from 4 pairs of pants, 6 shirts, and 2 pairs of shoes for an interview. If an outfit consists of 1 pair of pants, 1 pair of shoes, and 1 shirt, how many options does she have?

Possible Answers:

120

Correct answer:

Explanation:

To find total number, multiply the number of each item.

(6)(4)(2)=48

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Example Question #1 : Integers And Types Of Numbers

What is the greatest prime factor of (3^7)(5^8)?

Possible Answers:

Correct answer:

Explanation:

The only prime factors are 3 and 5, therefore, 5 will be the greatest prime factor.

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Example Question #4 : Properties Of Integers

Solve:

$(8\times 10^6)+(5\times 10^4)+(3\times 10^3)+(4\times 10^2)+(6\times 10)+(7\times 10^0)=$

Possible Answers:

800,053,467

853,467

8,053,467

80,053,467

Correct answer:

8,053,467

Explanation:

$8\times 10^6=8,000,000$

$5\times 10^4=50,000$

$3\times 10^3=3,000$

$4\times 10^2=400$

$6\times 10=60$

$7\times 10^0=7$

The sum is 8,053,467

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Example Question #3 : Properties Of Integers

If a positive integer is divided by another positive integer , then the quotient is 6, and there is no remainder.

Which of these choices is a possible value of M + N ?

Possible Answers:

784

392

Each of the other choices is a possible value of M + N .

Correct answer:

Each of the other choices is a possible value of M + N .

Explanation:

The conditions of the problem can be rewritten as $N \div M = 6$ , or N =6M .

M + N = M + 6M = 7M , meaning that the sum of the two numbers is a multiple of 7. Each of the given choices is a multiple of 7, so any of them can be M + N .

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Example Question #1 : Properties Of Integers

What is the first digit in the base-six representation of the number 936?

Possible Answers:

Correct answer:

Explanation:

216 < 936 < 1296 , or, equivalently, $6^{3}< 936 < 6^{4}$ . This makes 936 a four-digit number when written in base six. The first digit is equal to the number of times 216 divides into 936.

$936 \div 216 = 4 \textrm{ R } 72$ ,

4 is the first digit of this number.

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Example Question #1722 : Problem Solving Questions

What is the last digit in the base-eight representation of the number 735?

Possible Answers:

Correct answer:

Explanation:

Divide 735 by 8. The remainder is the last digit of the base-eight representation.

$735 \div 8 = 91 \textrm{ R } 7$

The correct choice is 7.

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Example Question #1723 : Problem Solving Questions

You are given that the product of eight numbers, each of which is nonzero, is positive. Which of the following is not possible?

Possible Answers:

Each of the scenarios in the other choices is possible.

All of the numbers are negative.

Exactly two of the numbers are negative.

Exactly two of the numbers are positive.

Half of the numbers are positive and half are negative.

Correct answer:

Each of the scenarios in the other choices is possible.

Explanation:

The product of a group of nonzero numbers is positive if and only if an even number of these factors is negative. This occurs in each of these scenarios.

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Example Question #1724 : Problem Solving Questions

A one-hundred-digit integer that is divisible by 6 begins with a 1; its next ninety-seven digits are all zeroes. Which of the following could be its last two digits?

Possible Answers:

Correct answer:

Explanation:

For a number to be divisible by 6, it must be both even and a multiple of 3. None of the choices can be eliminated by that first criterion. But to fit the second criterion, the digit sum must be divisible by 3. We need only add the nonzero digits of each choice, remembering to include the leading 1 in the sum:

42: 1 + 4 + 2 = 7

52: 1 + 5 + 2 = 8

56: 1 + 5 + 6 = 12

66: 1 + 6 + 6 = 13

76: 1 + 7 + 6 = 14

Of these choices, only 56 passes the divisibility test, so it is the correct choice.

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Integers And Types Of Numbers

Example Question #2 : Properties Of Integers

Example Question #1721 : Problem Solving Questions

Example Question #1 : Integers And Types Of Numbers

Example Question #4 : Properties Of Integers

Example Question #3 : Properties Of Integers

Example Question #1 : Properties Of Integers

Example Question #1722 : Problem Solving Questions

Example Question #1723 : Problem Solving Questions

Example Question #1724 : Problem Solving Questions

All GMAT Math Resources

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