GMAT Math : Arithmetic

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Example Questions

Example Question #121 : Arithmetic

is 40% of . What percent of $N^{3}$ is $F^{3}$ ?

Possible Answers:

The correct answer is not among the other responses.

$13 \frac{1}{3} \%$

$64 \%$

$120 \%$

$6 \frac{2}{5 } \%$

Correct answer:

$6 \frac{2}{5 } \%$

Explanation:

If is 40% of , then $F = \frac{40}{100} N = \frac{2}{5} N$ .

Cube both sides to get

$F^{3} = \left (\frac{2}{5} N \right )^{3}$

$F^{3} = \frac{8}{125} N ^{3}$

$F^{3}$ is $\frac{8}{125}$ of $N ^{3}$ , or equivalently,

$F^{3}$ is $\frac{8}{125} \times 100 \% = 6 \frac{2}{5 } \%$ of $N ^{3}$ .

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Example Question #122 : Arithmetic

$\sqrt{t}$ is 36% of $\sqrt{r}$ . What percent of is ?

Possible Answers:

$6 \%$

The correct answer is not given among the other responses.

$72 \%$

$36 \%$

$18 \%$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

$\sqrt{t}$ is 36% of $\sqrt{r}$ , so

$\sqrt{t} = \frac{36}{100} \sqrt{r}$ , or

$\sqrt{t} = \frac{9}{25} \sqrt{r}$

Square both sides:

$\left (\sqrt{t} \right )^{2}= \left (\frac{9}{25} \sqrt{r} \right )^{2}$

$t= \frac{81}{625} r$

is $\frac{81}{625}$ of , or, equivalently, $\frac{81}{625} \times 100 \% = 12 \frac{24}{25} \%$ of .

This answer is not among the given choices.

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Example Question #1672 : Problem Solving Questions

is 40% of .

is what percent of 2S + P ?

Possible Answers:

$41 \frac{2}{3}\%$

$180 \%$

$450 \%$

$22 \frac{2}{9}\%$

$55 \frac{5}{9} \%$

Correct answer:

$22 \frac{2}{9}\%$

Explanation:

is 40% of , so $S = \frac{40}{100}P = \frac{2}{5}P$ .

Eqivalently,

$P = \frac{5}{2}S$ , and

$2S + P = 2S +\frac{5}{2}S = \frac{9}{2}S$ .

The question can be restated as

is what percent of $\frac{9}{2}S$ ?

This can be answered as

$\frac{S}{\frac{9}{2}S} \times 100 \% = \frac{2}{9} \times 100 \% = 22 \frac{2}{9} \%$ .

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Example Question #46 : Percents

is 20 % of .

N - M is what percent of N + M ?

Possible Answers:

$66 \frac{2}{3} \%$

$120 \%$

$80 \%$

$62\frac{1}{2} \%$

$150 \%$

Correct answer:

$66 \frac{2}{3} \%$

Explanation:

is 20% of , so $M = \frac{20}{100}N= \frac{1}{5}N$ .

$N - M = N - \frac{1}{5}N = \frac{4}{5}N$

$N +M = N + \frac{1}{5}N = \frac{6}{5}N$

The question can be rewritten as

$\frac{4}{5}N$ is what percent of $\frac{6}{5}N$ ?

The answer is found as follows:

$\frac{\frac{4}{5}N}{\frac{6}{5}N} \times 100 \% = \frac{4}{6} \times 100 \% = 66 \frac{2}{3} \%$

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Example Question #1673 : Problem Solving Questions

M -N is 75% of .

is what percent of M + N ?

Possible Answers:

$75 \%$

$56\frac{1}{4}\%$

$62\frac{1}{2} \%$

$80 \%$

$66 \frac{2}{3}\%$

Correct answer:

$80 \%$

Explanation:

M -N is 75% of , so

$M -N = \frac{3}{4}M$

and

$\frac{1}{4}M = N$

$M + N = M +\frac{1}{4}M = \frac{5}{4}M$

The question can be rewritten as

is what percent of $\frac{5}{4}M$ ?

The answer is found as follows:

$\frac{N}{\frac{5}{4}N} \times 100 \% = \frac{4}{5} \times 100 \% = 80 \%$ .

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Example Question #1674 : Problem Solving Questions

To the nearest whole number, what percent of 5 is 40?

Possible Answers:

$800\%$

$80\%$

$8\%$

$1.25\%$

$125\%$

Correct answer:

$800\%$

Explanation:

To calculate percent, we need to take one number and divide it by the other. We need to plan out the order carefully, though, because doing the division backwards will yield a trap answer.

We need to find what percent of 5 40 is. It needs to be greater than 100%, because 40 is larger than five. This clues us in that 40 needs to be in our numerator. Perform the following to solve:

$\frac{40}{5}=8$

Don't stop just yet though, because to convert from decimals to percents we need to multiply by 100. This makes our final answer 800%. So, we can say the 40 is 800% of 5.

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Example Question #1671 : Problem Solving Questions

To the nearest whole percent, what percent of 108 is 69?

Possible Answers:

$16\%$

$156\%$

$64\%$

$32\%$

$69\%$

Correct answer:

$64\%$

Explanation:

To find percents, simply divide the part by the whole. In this case, we are asked to find what percent 69 is of 108. Take 69 over 108 to find the answer.

$\small \frac{69}{108}=.638\bar{8}$

Multiply by 100 and round to get our final answer

$\small \small .63\bar{8}*100=63.8 \approx 64$

So, the answer is 64%.

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Example Question #1676 : Problem Solving Questions

After receiving a 25 % % discount on an item, Paola saved $\$ 68.75$ . What was the original price?

Possible Answers:

$\$ \ 275.00$

$\$ \ 171.87$

$\$ \ 1718.75$

$\$ \ 206.00$

Correct answer:

$\$ \ 275.00$

Explanation:

We can set up an equation to solve this problem where represents the orignal price:

$0.25 \ p=68.75$

That is, % of a number equals the $\$ 68.75$ she saved. Now we just have to solve for :

$p=\frac{68.75}{0.25}= 275$

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Example Question #51 : Calculating Percents

Anthony is trying to decide if he should use a coupon for $\$ 20$ off or a coupon for a % discount on the same item. The item costs $\$145$ before any discounts are applied. Which coupon will save him the most money?

Possible Answers:

The % discount code

Both will save Anthony the same amount

$\$ 20$ off coupon

Correct answer:

The % discount code

Explanation:

In order to solve this problem we need to know how much he'll be saving when he uses each:

We already know he can save $\$ 20$ with a coupon but what about the discount code?

(0.15)(145)=21.75

So, using the discount code he would save $\$1.75$ more than using the coupon

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Example Question #51 : Percents

In a bag, Mary has red marbles, blue marbles, and green marbles. What percent of the marbles are red?

Possible Answers:

$10\%$

$20\%$

$50\%$

$60\%$

$40\%$

Correct answer:

$40\%$

Explanation:

To calculate the percentage, you must first find the fraction of marbles that are red and then convert the fraction to a percent.

$\% \textup{red }= \frac{32}{32+40+8}=\frac{32}{80}=\frac{4}{10}=40\%$

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #121 : Arithmetic

Example Question #122 : Arithmetic

Example Question #1672 : Problem Solving Questions

Example Question #46 : Percents

Example Question #1673 : Problem Solving Questions

Example Question #1674 : Problem Solving Questions

Example Question #1671 : Problem Solving Questions

Example Question #1676 : Problem Solving Questions

Example Question #51 : Calculating Percents

Example Question #51 : Percents

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