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SSAT Middle Level Math : Percentage

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Example Questions

Example Question #51 : Percentage

Rectangle 1

The above rectangle is divided into squares of equal size. What percent of the rectangle is shaded in?

Possible Answers:

$72 \%$

$80\%$

$75 \%$

$60 \%$

Correct answer:

$80\%$

Explanation:

8 of the 10 squares - $\frac{8}{10}$ of the rectangle - is shaded in, so

$\frac{8}{10} \times 100 \% = \frac{800}{10} \% = 80 \%$

of rectangle is shaded.

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Example Question #52 : Percentage

Assorted 1

What percent of the above figures have been shaded in?

Possible Answers:

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

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

$58 \frac{1}{3} \%$

$33 \frac{1}{3} \%$

Correct answer:

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

Explanation:

There are twelve figures, five of which have been shaded in, so $\frac{5}{12}$ of the figures are shaded; this is

$\frac{5}{12} \times 100 \% = \frac{500}{12} \% = \frac{125}{3} \%$

Since $125\div 3 = 41 \textrm{ R }2$ , this is equal to $41 \frac{2}{3} \%$ of the figure.

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Example Question #53 : Percentage

is 30% of and 60% of .

What percent of is ?

Possible Answers:

$90 \%$

$50 \%$

$200 \%$

$30 \%$

Correct answer:

$50 \%$

Explanation:

is 30% of , so

$F = \frac{30}{100}G$

$F = \frac{3}{10}G$

$\frac{10} {3} \cdot F = \frac{10} {3} \cdot \frac{3}{10}G$

$\frac{10} {3} F = G$

is 60% of , so

$F = \frac{60}{100}H$

$F = \frac{3}{5}H$

$\frac{5} {3} \cdot F = \frac{5} {3} \cdot \frac{3}{5}H$

$\frac{5} {3} F = H$

To determine what percent of is, evaluate:

$\frac{H}{G} \cdot 100 \%$

$=\frac{\frac{5} {3} F }{ \frac{10} {3} F} \cdot 100 \%$

$=\frac{\frac{5} {3} }{ \frac{10} {3} } \cdot 100 \%$

$= \frac{5} {3} \cdot \frac {3}{10} \cdot 100 \%$

$= \frac{1,500} {30} \%$

$= 50 \%$

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Example Question #52 : Percentage

Assorted 1

What percent of the above figures are circles?

Possible Answers:

$25 \%$

$50 \%$

$75 \%$

$40 \%$

Correct answer:

$50 \%$

Explanation:

There are twelve figures, six of which are circles. This is

$\frac{6}{12} \times 100 \% = \frac{600}{12} \% = 50 \%$

of the figures.

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Example Question #55 : Percentage

is $\frac{1}{2} \%$ of .

is 2.5 % of .

What percent of is ?

Possible Answers:

$20 \%$

$500 \%$

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

$5 \%$

Correct answer:

$500 \%$

Explanation:

For the sake of simplicity, since this reasoning is independent of the actual value of , we will assume that C = 100 . Then is $\frac{1}{2} \%$ of 100, or simply $\frac{1}{2} = 0.5$ , and is 2.5% of 100, or simply 2.5. To find out what percent is of , evaluate:

$\frac{B}{A} \cdot 100 \% = \frac{2.5}{0.5} \cdot 100 \% = 5 \cdot 100 \% = 500 \%$

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Example Question #56 : Percentage

is 20% of and $\frac{1}{4} \%$ of .

What percent of is ?

Possible Answers:

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

$8,000 \%$

$80 \%$

$5 \%$

Correct answer:

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

Explanation:

20% of a number is $\frac{20}{100} = \frac{1}{5}$ of that number, so $S = \frac{1}{5} T$ . Equivalently,

$5 \cdot S =5 \cdot \frac{1}{5} T$

5S = T

$\frac{1}{4} \%$ of a number is $\frac{\frac{1}{4}}{100} = \frac{1}{4} \div 100 = \frac{1}{4} \times \frac{1}{100} = \frac{1}{4 00}$ of that number, so $S = \frac{1}{400 } U$ . Equivalently,

$400 \cdot S =400 \cdot \frac{1}{400 } U$

400 S = U

To find out what percent is of , evaluate:

$\frac{T}{U}\cdot 100 \% = \frac{5S}{400S} \cdot 100 \% = \frac{5}{400} \cdot 100 \% = \frac{500}{400} \% = \frac{5}{4} \% = 1 \frac{1}{4} \%$

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Example Question #57 : Percentage

is 40% of . is 72% of .

What percent of is ?

Possible Answers:

$180 \%$

$112 \%$

$32 \%$

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

Correct answer:

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

Explanation:

is 40 % of , or $K = \frac{40}{100} L$ ; is 72% of , or $M = \frac{72}{100} L$ .

To find out what percent is of , evaluate:

$\frac{K}{M} \cdot 100 \%$

$= \frac{ \frac{40}{100} L }{ \frac{72}{100} L} \cdot 100 \%$

$= \frac{ \frac{40}{100} }{ \frac{72}{100} } \cdot 100 \%$

$= \frac{40 }{ 72} \cdot 100 \%$

$= \frac{5}{9} \cdot 100 \%$

$= \frac{500}{9} \%$

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

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SSAT Middle Level Math : Percentage

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #51 : Percentage

Example Question #52 : Percentage

Example Question #53 : Percentage

Example Question #52 : Percentage

Example Question #55 : Percentage

Example Question #56 : Percentage

Example Question #57 : Percentage

All SSAT Middle Level Math Resources

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