GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #11 : Understanding Fractions

Casius has $\tiny \frac{1}{6}$ of a liter of water. Olivar has $\tiny \frac{4}{7}$ of the amount Casius has. How many liters of water does Olivar have?

Possible Answers:

$\tiny \tiny \frac{7}{6}$

$\tiny \tiny \frac{1}{4}$

$\tiny \tiny \frac{6}{7}$

$\tiny \frac{2}{21}$

$\tiny \frac{7}{24}$

Correct answer:

$\tiny \frac{2}{21}$

Explanation:

This question tests your ability to read word problems and multiply fractions. Because we know that Olivar has $\frac{4}{7}$ of what Casius has, we can see that we need to multiply. Perform the following operation to find the answer.

$\frac{1}{6}*\frac{4}{7}=\frac{4}{42}=\frac{2}{21}$

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Example Question #15 : Understanding Fractions

Define an operation $\ast$ as follows:

For all real numbers a ,b ,

$a \ast b = 2a \div b$

Evaluate $5\frac{1}{6} \ast 3\frac{1}{3}$ , and round to the nearest whole number.

Possible Answers:

Correct answer:

Explanation:

$a \ast b = 2a \div b$

$5\frac{1}{6} \ast 3\frac{1}{3} = 2 \left ( 5\frac{1}{6} \right ) \div 3\frac{1}{3}$

$= 2 \left ( \frac{31}{6} \right ) \div \frac{10}{3}$

$= \frac{31}{3} \div \frac{10}{3}$

$= \frac{31}{3} \cdot \frac{3}{10}$

$= \frac{31} {10}$

$=3 \frac{1} {10}$

This rounds to 3.

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Example Question #11 : Fractions

Seven thirds of eighteen seventieths is what?

Possible Answers:

Seven fifths

Five thirds

Three fifths

Seven sixths

Three sevenths

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 #12 : Fractions

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 #21 : Understanding Fractions

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

Possible Answers:

$\frac{ycd}{xab}$

$\frac{xab}{ycd}$

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

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

Not enough information provided.

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 #373 : Arithmetic

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:

Yes

No, because she does not have enough sugar or flour

No, because she does not have enough sugar or chocolate

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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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Understanding Fractions

Example Question #15 : Understanding Fractions

Example Question #11 : Fractions

Example Question #12 : Fractions

Example Question #11 : Fractions

Example Question #15 : Understanding Fractions

Example Question #18 : Understanding Fractions

Example Question #21 : Understanding Fractions

Example Question #372 : Arithmetic

Example Question #373 : Arithmetic

All GMAT Math Resources

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