GRE Math : Arithmetic

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Example Questions

Example Question #1 : How To Express A Fraction As A Ratio

Express $\frac{5}{6}$ as a ratio.

Possible Answers:

1.5:1.6

$\frac{1}{5}:\frac{1}{6}$

0.6:0.5

6:5

5:6

Correct answer:

5:6

Explanation:

A ratio is two numbers separated by a colon. When expressing fractions as a ratio, the numerator is the number to the left of the colon while the denominator is to the right of the colon. The answer is 5:6.

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Example Question #2 : How To Express A Fraction As A Ratio

If there are fifteen girls and six boys in a class, what is the ratio of boys to girls?

Possible Answers:

21:6

6:15

15:6

6:21

15:21

Correct answer:

6:15

Explanation:

Let's convert the words into numbers. Since there are girls and boys, we need ratio of boys to girls. The ratio should be 6:15 .

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Example Question #2 : How To Express A Fraction As A Ratio

What is the ratio of square numbers to cubic numbers from 1-30 noninclusive?

Possible Answers:

2:3

2:1

5:3

1:2

3:5

Correct answer:

2:1

Explanation:

Let's list a bunch of square numbers from 1-30 noninclusive.

doesn,t count since it's not included HOWEVER: 4, 9, 16, 25 count.

Let's list a bunch of cubic numbers from 1-30 noninclusive.

doesn,t count since it's not included HOWEVER: 8, 27 count.

There are four square numbers to two cubic numbers. The ratio becomes 4:2 or 2:1 .

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Example Question #2 : How To Express A Fraction As A Ratio

If apples equal bananas and bananas equal carrots, what is the ratio of an apple to a carrot?

Possible Answers:

4:3

8:9

2:3

9:8

3:4

Correct answer:

9:8

Explanation:

To get the apple to carrot ratio, we need to equal out the bananas. The least common denominator of and is . So if apples equal bananas, then bananas equal apples. Also, if bananas equal carrots, then bananas equal carrots. Since now the total bananas are equal, we can find the ratio of apples to carrots. We have 9:8 as the final answer.

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Example Question #61 : Proportion / Ratio / Rate

Convert 0.57:0.95 into reduced fraction form.

Possible Answers:

$\frac{3}{8}$

$\frac{3}{5}$

$\frac{57}{95}$

$\frac{5}{3}$

$\frac{95}{57}$

Correct answer:

$\frac{3}{5}$

Explanation:

We can rewrite the ratio 0.57:0.95 as a fraction. The first number in the ratio is in the numerator while the second number in the ratio is in the denominator.

$\frac{0.57}{0.95}=\frac{57}{95}=\frac{3}{5}$ Remember to get rid of decimals, we can move the decimal point two places to the right. Afterwards, the two numbers are divisible by .

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Example Question #12 : How To Express A Fraction As A Ratio

Express $\frac{1}{2}:\frac{1}{3}$ as an integer ratio.

Possible Answers:

5:6

3:2

2:3

1:1

0.5:0.333

Correct answer:

3:2

Explanation:

To find an integer ratio, let's find the fractions with a common denominator. This will be . Then, we multiply the left by and the right by to get fractions of $\frac{3}{6}$ and $\frac{2}{6}$ . With the same denominators, we just have numerators to compare. Ratio is then 3:2 .

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Example Question #561 : Arithmetic

If the ratio of girls to boys is 7:6 , what could be the number of children in the class?

Possible Answers:

Correct answer:

Explanation:

If there are girls and boys, that means we have students in the class. To continue to have this ratio, we need an answer than is a multiple of .

is a multiple of which is the right answer.

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Example Question #14 : How To Express A Fraction As A Ratio

An espresso drink has a ratio of 3:7 ounces of espresso to water. If Amanda wants her drink to be $25\%$ espresso, how much water was added?

Possible Answers:

Correct answer:

Explanation:

In the problem, the drink is $30\%$ espresso since the overall weight of the drink is ounces. If we are reducing the concentration of espresso to $25\%$ , then we can create an equation to figure out the addition of water.

$\frac{3}{10+x}=\frac{1}{4}$ represents the addition of water.

Cross-multiply.

12=10+x

Subtract on both sides.

x=2

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Example Question #11 : How To Express A Fraction As A Ratio

If Jill, Jack and John found $\$1000$ and decided to split it 6:9:5 respectively, how much more did Jack get than John?

Possible Answers:

250

450

200

300

150

Correct answer:

200

Explanation:

If Jill, Jack and John get 6:9:5 , that means there are parts.

Because they found 1000 , each part gets $\frac{1000}{20}$ or $\$50$ .

Jack gets $50\cdot9$ or $\$450$ .

John gets $50\cdot5$ or $\$250$ .

Since the question is asking how much more did Jack get than John, we subtract 450 and 250 to get 200 .

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Example Question #16 : How To Express A Fraction As A Ratio

If there are 500 dolls and $96\%$ of them are not broken, what's the ratio of broken dolls to unbroken dolls?

Possible Answers:

1:25

24:1

1:24

25:1

24:25

Correct answer:

1:24

Explanation:

You don't need to solve for the actual number of broken or unbroken dolls. Instead, put the percentages in the ratio because no matter what, the percentages are fixed regardless of amount of dolls broken or unbroken.

So the question is asking for broken to unbroken. The percentage of broken dolls is $4\%$ .

So we have a ratio of 4:96 or 1:24 .

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GRE Math : Arithmetic

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Express A Fraction As A Ratio

Example Question #2 : How To Express A Fraction As A Ratio

Example Question #2 : How To Express A Fraction As A Ratio

Example Question #2 : How To Express A Fraction As A Ratio

Example Question #61 : Proportion / Ratio / Rate

Example Question #12 : How To Express A Fraction As A Ratio

Example Question #561 : Arithmetic

Example Question #14 : How To Express A Fraction As A Ratio

Example Question #11 : How To Express A Fraction As A Ratio

Example Question #16 : How To Express A Fraction As A Ratio

All GRE Math Resources

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