GMAT Math : Arithmetic

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Example Questions

Example Question #1921 : Problem Solving Questions

Seven thirds of eighteen seventieths is what?

Possible Answers:

Seven sixths

Five thirds

Seven fifths

Three sevenths

Three fifths

Correct answer:

Three fifths

Explanation:

Seven thirds of eighteen seventieths is

$\frac{7}{3} \times \frac{18 }{70} = \frac{7}{3} \times \frac{9}{35} = \frac{1}{1} \times \frac{3}{5}= \frac{3}{5}$

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Example Question #1922 : Problem Solving Questions

One orange yields $\frac{1}{3}$ cup of juice; one gallon is equal to 16 cups. How many oranges are needed to yield one half gallon of orange juice?

Possible Answers:

Correct answer:

Explanation:

One half gallon comprises 8 cups. To find the number of oranges needed, divide:

$8 \div \frac{1}{3} = 24$

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Example Question #11 : Fractions

Raise $\frac{15}{75}$ to the fourth power and express the result in lowest terms.

Possible Answers:

$\frac{1}{625}$

$\frac{1}{216}$

$\frac{1}{256}$

$\frac{1}{1,296}$

$\frac{1}{125}$

Correct answer:

$\frac{1}{625}$

Explanation:

$\frac{15}{75}$ reduces to $\frac{15 \div 15}{75 \div 15} = \frac{1}{5}$ . Raise this to the fourth power:

$\left ( \frac{1}{5} \right )^{4} = \frac{1}{5^{4}} = \frac{1}{625}$

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Example Question #15 : Understanding Fractions

Evaluate: $\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}$

Possible Answers:

$\frac{1,296}{2,401}$

$-\frac{162}{2,401}$

$-\frac{1,296}{2,401}$

$\frac{162}{2,401}$

Correct answer:

$\frac{162}{2,401}$

Explanation:

$\left (\frac{3}{7} \right )^{4} = \frac{3^{4} }{7^{4} } = \frac{81 }{2,401}$

$\left (-\frac{3}{7} \right )^{4} =\left (\frac{3}{7} \right )^{4} = \frac{81 }{2,401}$

$\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}=\frac{81 }{2,401}+\frac{81 }{2,401}=\frac{162}{2,401}$

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Example Question #18 : Understanding Fractions

Evaluate: $-\left (\frac{5}{8} \right )^{4} + \left (-\frac{5}{8} \right )^{4}$

Possible Answers:

$-\frac{625}{4,096}$

$\frac{625}{4,096}$

Correct answer:

Explanation:

This can actually be solved without any calculation.

A negative number raised to an even power is equal to its absolute value raised to that power, so

$\left (-\frac{5}{8} \right )^{4} = \left (\frac{5}{8} \right )^{4}$

Therefore, we can replace:

$-\left (\frac{5}{8} \right )^{4} + \left (\frac{5}{8} \right )^{4} = \left (\frac{5}{8} \right )^{4} -\left (\frac{5}{8} \right )^{4} =0$

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Example Question #1921 : Problem Solving Questions

Simplify the following into a single fraction: $\frac{x}{y}+\frac{ab}{cd}$

Possible Answers:

Not enough information provided.

$\frac{ycd}{xcd+yab}$

$\frac{xcd+yab}{ycd}$

$\frac{ycd}{xab}$

$\frac{xab}{ycd}$

Correct answer:

$\frac{xcd+yab}{ycd}$

Explanation:

In order to simplify $\frac{x}{y}+\frac{ab}{cd}$ , combine the terms by finding the common denominator:

$\frac{x}{y}+\frac{ab}{cd}$

$=\frac{x(cd)}{y(cd)}+\frac{(y)ab}{(y)cd}$

$=\frac{xcd+yab}{ycd}$

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Example Question #372 : Arithmetic

Simplify the following expression: $\frac{5}{6}+\frac{7}{11}+\frac{4}{3}$

Possible Answers:

$\frac{181}{61}$

$\frac{185}{66}$

$\frac{184}{62}$

$\frac{182}{64}$

$\frac{183}{69}$

Correct answer:

$\frac{185}{66}$

Explanation:

In order to simplify the expression, we start by finding the common denominator of each term in $\frac{5}{6}+\frac{7}{11}+\frac{4}{3}$ :

In this case the common denominator is 66.

$\frac{5}{6}\left(\frac{11}{11} \right )+\frac{7}{11}\left(\frac{6}{6} \right )+\frac{4}{3}\left(\frac{22}{22} \right )$

$=\frac{55}{66}+\frac{42}{66}+\frac{88}{66}$

$=\frac{55+42+88}{66}$

$=\frac{185}{66}$

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Example Question #21 : Fractions

Clara wants to make sixteen batches of her world famous Icky Sticky Ooey Gooey Chocolate Bomb Brownies. Each batch of brownies requires $\frac{3}{4}$ cups of flour, $1\frac{1}{2}$ cups of sugar, and $1\frac{3}{4}$ cups of bittersweet chocolate.

She has 14 cups of flour, 22 cups of sugar, and 25 cups of bittersweet chocolate on hand; assuming other ingredients are not an issue, can Clara make sixteen batches of brownies?

Possible Answers:

No, because she does not have enough sugar or chocolate

No, because she does not have enough sugar or flour

Yes

No, because she does not have enough flour or chocolate

No, because she does not have enough flour, sugar, or chocolate

Correct answer:

No, because she does not have enough sugar or chocolate

Explanation:

To make sixteen batches of brownies, Clara will require:

$\frac{3}{4} \times 16 = 12$ cups of flour; since Clara has 14 cups on hand, she has sufficient flour.

$1\frac{1}{2} \times 16 = 24$ cups of sugar; since Clara has 22 cups on hand, she needs more sugar.

$1\frac{3}{4} \times 16 = 28$ cups of bittersweet chocolate; since Clara has 25 cups on hand, she needs more bittersweet chocolate.

The correct choice is that she cannot make them, since she does not have enough sugar or chocolate.

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Example Question #1931 : Gmat Quantitative Reasoning

Suzanne wants to make fifteen batches of her world famous Icky Sticky Ooey Gooey Oatmeal Peanut Butter Cookies. Each batch of cookies requires $1\frac{1}{2}$ cups of flour, $1\frac{1}{4}$ cups of sugar, and $1\frac{3}{4}$ cups of oatmeal, among other ingredients.

She has 20 cups of flour, 24 cups of sugar, and 30 cups of oatmeal on hand; assuming other ingredients are not an issue, can Suzanne make fifteen batches of brownies?

Possible Answers:

No, because she does not have enough oatmeal

No, because she does not have enough flour

Yes

No, because she does not have enough flour, sugar, or oatmeal

No, because she does not have enough sugar

Correct answer:

No, because she does not have enough flour

Explanation:

To make fifteen batches of cookies, Suzanne will require:

$1\frac{1}{2} \times 15 = 22 \frac{1}{2}$ cups of flour; since Suzanne has 20 cups on hand, she needs more flour.

$1\frac{1}{4} \times 15 = 18 \frac{3}{4}$ cups of sugar; since Suzanne has 24 cups on hand, she has sufficient sugar.

$1\frac{3}{4} \times 15 = 26 \frac{1}{4}$ cups of oatmeal; since Suzanne has 30 cups on hand, she has sufficient oatmeal.

The correct choice is that she cannot make them, since she does not have enough flour.

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Example Question #21 : Understanding Fractions

Three fifths of a number is twenty greater than one tenth of the same number. What is that number?

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{1}{10}N + 20 = \frac{3}{5} N$

$10 \cdot \left ( \frac{1}{10}N + 20 \right )= 10 \cdot \frac{3}{5} N$

N + 200 = 6N

200 = 5N

N = 40

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1921 : Problem Solving Questions

Example Question #1922 : Problem Solving Questions

Example Question #11 : Fractions

Example Question #15 : Understanding Fractions

Example Question #18 : Understanding Fractions

Example Question #1921 : Problem Solving Questions

Example Question #372 : Arithmetic

Example Question #21 : Fractions

Example Question #1931 : Gmat Quantitative Reasoning

Example Question #21 : Understanding Fractions

All GMAT Math Resources

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