GRE Math : How to find the part from the whole

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Example Questions

Example Question #1 : How To Find The Part From The Whole

Quantitative Comparison

Quantity A: 10% of $45

Quantity B: 45% of $10

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined from the information given.

Correct answer:

The two quantities are equal.

Explanation:

Quantity A: .1 * 45 = $4.50

Quantity B: .45 * 10 = $4.50

Therefore the two quantities are equal. This is always true: a% of $b = b% of $a.

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Example Question #1 : How To Find The Part From The Whole

What percent of 5 is $\displaystyle a$?

Possible Answers:

20a $\displaystyle 20a$

$\frac{a}{50}$ $\displaystyle \frac{a}{50}$

10a $\displaystyle 10a$

$\displaystyle 2a$

$\frac{a}{10}$ $\displaystyle \frac{a}{10}$

Correct answer:

20a $\displaystyle 20a$

Explanation:

$a=\frac{x}{100}\cdot 5\Rightarrow a=\frac{x}{20}\Rightarrow x=20a$ $\displaystyle a=\frac{x}{100}\cdot 5\Rightarrow a=\frac{x}{20}\Rightarrow x=20a$

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Example Question #2 : How To Find The Part From The Whole

Quantity A:

$\displaystyle x$, where $\displaystyle x$ is $27\%$ $\displaystyle 27\%$ of 150 $\displaystyle 150$

Quantity B:

$\displaystyle y$, where $\displaystyle y$ is $94\%$ $\displaystyle 94\%$ of $\displaystyle 75$

Which of the following is true?

Possible Answers:

A comparison cannot be detemined from the given information.

The two quantities are equal.

Quantity B is larger.

Quantity A is larger.

Correct answer:

Quantity B is larger.

Explanation:

This type of problem is very easy. You merely need to translate the text into the form of an equation. For this, remember that "of" is translated as multiplication and "is" as equality. This gives us the following.

Quantity A:

$\displaystyle x$ is $27\%$ $\displaystyle 27\%$ of 150 $\displaystyle 150$

Becomes...

$x = 0.27 \cdot 150=40.5$ $\displaystyle x = 0.27 \cdot 150=40.5$

Quantity B:

$\displaystyle y$ is $94\%$ $\displaystyle 94\%$ of $\displaystyle 75$

Becomes...

$y = 0.94 \cdot 75 = 70.5$ $\displaystyle y = 0.94 \cdot 75 = 70.5$

Therefore, quantity B is larger.

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Example Question #3 : How To Find The Part From The Whole

Quantity A:

$\displaystyle x$, where $\displaystyle x$ is $91\%$ $\displaystyle 91\%$ of 228 $\displaystyle 228$

Quantity B:

$\displaystyle y$, where $\displaystyle y$ is $95\%$ $\displaystyle 95\%$ of 220 $\displaystyle 220$

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity A is larger.

Quantity B is larger.

A comparison cannot be detemined from the given information.

Correct answer:

Quantity B is larger.

Explanation:

Quantity A:

$\displaystyle x$ is $91\%$ $\displaystyle 91\%$ of 228 $\displaystyle 228$

Becomes...

$x = 0.91 \cdot 228 = 207.48$ $\displaystyle x = 0.91 \cdot 228 = 207.48$

Quantity B:

$\displaystyle y$ is $95\%$ $\displaystyle 95\%$ of 220 $\displaystyle 220$

Becomes...

$y = 0.95 \cdot 220 = 209$ $\displaystyle y = 0.95 \cdot 220 = 209$

Therefore, quantity B is larger.

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Example Question #4 : How To Find The Part From The Whole

Quantity A:

$\displaystyle x$, where $\displaystyle x$ is $65\%$ $\displaystyle 65\%$ of 408 $\displaystyle 408$

Quantity B:

$\displaystyle y$, where $\displaystyle y$ is $40\%$ $\displaystyle 40\%$ of 663 $\displaystyle 663$

Which of the following is true?

Possible Answers:

Quantity A is greater.

A comparison cannot be detemined from the given information.

The two quantities are equal.

Quantity B is greater.

Correct answer:

The two quantities are equal.

Explanation:

Quantity A:

$\displaystyle x$ is $65\%$ $\displaystyle 65\%$ of 408 $\displaystyle 408$

Becomes...

$x = 0.65 \cdot 408 = 265.2$ $\displaystyle x = 0.65 \cdot 408 = 265.2$

Quantity B:

$\displaystyle y$ is $40\%$ $\displaystyle 40\%$ of 663 $\displaystyle 663$

Becomes...

$y = 0.4 \cdot 663 = 265.2$ $\displaystyle y = 0.4 \cdot 663 = 265.2$

Therefore, the two quantities are equal.

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Example Question #6 : Whole And Part

A bag contains $\textup{500 coins}$ $\displaystyle \textup{500 coins}$. $25\%$ $\displaystyle 25\%$ are quarters, $15\%$ $\displaystyle 15\%$ are dimes and the rest are nickels. How much money is in the bag in nickels?

Possible Answers:

$\$31.25$ $\displaystyle \$31.25$

$\$20$ $\displaystyle \$20$

$\$14$ $\displaystyle \$14$

$\$7.50$ $\displaystyle \$7.50$

$\$15$ $\displaystyle \$15$

Correct answer:

$\$15$ $\displaystyle \$15$

Explanation:

To solve this problem we must first find what percent of the money in the bag is in nickels. We know that combined, quarters and dimes make up 40% of the coins and that the rest are nickels. Therefore 60% of the money in the bag are nickels. We then multiply the total amount of coins in the bag with that percentage in order to find out how many nickels are in the bag. $\displaystyle 500*0.6=300$. There are 300 nickels in the bag and nickels are worth 5 cents each. Therefore $300*0.05=15 \textup{ dollars}$ $\displaystyle 300*0.05=15 \textup{ dollars}$ worth of nickels in the bag.

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GRE Math : How to find the part from the whole

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Part From The Whole

Example Question #1 : How To Find The Part From The Whole

Example Question #2 : How To Find The Part From The Whole

Example Question #3 : How To Find The Part From The Whole

Example Question #4 : How To Find The Part From The Whole

Example Question #6 : Whole And Part

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