GRE Math : How to find a fraction from a percentage

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find A Fraction From A Percentage

Column A: \(\displaystyle \frac{2}{5}\%\)                                                                                                                                                                               

Column B: \(\displaystyle 0.40\)

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the given information.

Column A is greater.

Column B is greater.

Correct answer:

Column B is greater.

Explanation:

2/5% = 0.40% = 0.004.  Therefore, Column B is greater.

Example Question #4 : Percentage

\(\displaystyle a\) is \(\displaystyle 15\) percent of \(\displaystyle 20\)

\(\displaystyle 7\) is \(\displaystyle b\) percent of \(\displaystyle 140\)

Quantity A: \(\displaystyle a\)

Quantity B: \(\displaystyle b\)

Possible Answers:

Quantity A is greater.

The relationship cannot be determined.

The two quantities are equal.

Quantity B is greater.

Correct answer:

Quantity B is greater.

Explanation:

To do this problem, translate each expression into mathematical terms:

\(\displaystyle a\) is \(\displaystyle 15\) percent of \(\displaystyle 20\):

\(\displaystyle a=\frac{15}{100}(20)=\frac{300}{100}=3\)

\(\displaystyle 7\) is \(\displaystyle b\) percent of \(\displaystyle 140\):

\(\displaystyle 7=\frac{b}{100}(140)=b\frac{140}{100}\)

\(\displaystyle b=\frac{100}{140}(7)=\frac{100}{20}=5\)

Quantity B is greater.

Example Question #4 : Fractions And Percentage

Quantity A: 20% of \(\displaystyle \frac{3}{4}\)

Quantity B: 30% of \(\displaystyle \frac{5}{8}\)

Possible Answers:

Quantity A is greater.

The relationship cannot be determined.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

To solve this problem, consider writing the quantities in terms of only fractions:

Quantity A: 20% of \(\displaystyle \frac{3}{4}\)

\(\displaystyle \frac{20}{100}\frac{3}{4}=\frac{1}{5}\frac{3}{4}=\frac{3}{20}\)

 

Quantity B: 30% of \(\displaystyle \frac{5}{8}\)

\(\displaystyle \frac{30}{100}\frac{5}{8}=\frac{3}{10}\frac{5}{8}=\frac{3}{16}\)

Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.

Quantity B is greater.

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