GMAT Math : Arithmetic

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Example Questions

Example Question #1 : Properties Of Integers

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 #7 : 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 #1721 : Problem Solving Questions

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

80,053,467

853,467

8,053,467

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 #1 : 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:

392

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

784

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 #1725 : Problem Solving Questions

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 #1726 : 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 #171 : Arithmetic

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:

All of the numbers are negative.

Half of the numbers are positive and half are negative.

Each of the scenarios in the other choices is possible.

Exactly two of the numbers are positive.

Exactly two of the numbers 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 #11 : Properties Of Integers

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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Example Question #1731 : Problem Solving Questions

Express the quotient in scientific notation:

$\frac{ 5 \times 10^{18} }{ 8\times 10^{7} }$

Possible Answers:

$625 \times 10^{8}$

$\frac{ 5 }{ 8 } \times 10^{11}$

$0.625 \times 10^{11}$

$\frac{ 5\times 10^{11} }{ 8 }$

$6.25 \times 10^{10}$

Correct answer:

$6.25 \times 10^{10}$

Explanation:

All of these expressions are equivalent to the correct quotient. But a number in scientific notation takes the form

$a \times 10^{n}$ , where $1 \leq |a| < 10$

Only $6.25 \times 10^{10}$ takes this form.

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Example Question #1732 : Problem Solving Questions

Rewrite 117 as a number in base eight.

Possible Answers:

$163_{\textrm{eight}}$

$551_{\textrm{eight}}$

$155_{\textrm{eight}}$

$561 _{\textrm{eight}}$

$165_{\textrm{eight}}$

Correct answer:

$165_{\textrm{eight}}$

Explanation:

One way to do this:

Divide 117 by 8. The remainder will be the last digit.

$117 \div 8 = 14 \textrm{ R }5$

Now divide the quotient by 8. This remainder will be the second-to-last digit.

$14 \div 8 = 1 \textrm{ R }6$

The quotient is less than 8, so it will be the first digit. The base-eight equivalent of 117 is $165_{\textrm{eight}}$

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Properties Of Integers

Example Question #7 : Integers And Types Of Numbers

Example Question #1721 : Problem Solving Questions

Example Question #1 : Properties Of Integers

Example Question #1725 : Problem Solving Questions

Example Question #1726 : Problem Solving Questions

Example Question #171 : Arithmetic

Example Question #11 : Properties Of Integers

Example Question #1731 : Problem Solving Questions

Example Question #1732 : Problem Solving Questions

All GMAT Math Resources

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