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ISEE Middle Level Math : Percentage

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Example Questions

Example Question #161 : Percentage

A plane ticket is on sale for 25% its original price of $300.00. What is the sale price of the plane ticket?

Possible Answers:

$\$75$

$\$275$

$\$325$

$\$225$

Correct answer:

$\$225$

Explanation:

First, multiply: 300*0.25=75

Then, subtract that amount from the original price:

300-75=225

Answer: The plane ticket is on sale for $\$225.00$

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Example Question #162 : Percentage

A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10".

What percent of the balls are marked with an even number? Give the closest answer.

Possible Answers:

$55 \%$

$60 \%$

$45 \%$

$50 \%$

Correct answer:

$55 \%$

Explanation:

The number of balls in the box, in total, will be

1 + 2 + 3 + 4 + 5 + 6 + 7+ 8 + 9+ 10 = 55 balls,

of which

2 + 4 + 6 + 8 + 10 = 30

are even.

This is

$\frac{30}{55} \times 100 \% = 54 \frac{6}{11} \%$

This makes 55% the correct choice.

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Example Question #162 : Percentage

Assorted 1

What percent of the above figures are triangles?

Possible Answers:

$20 \%$

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

$16 \frac{2}{3 } \%$

$25 \%$

Correct answer:

$20 \%$

Explanation:

Of the fifteen figures, three are triangles - that is, $\frac{3}{15} = \frac{1}{5}$ of the figures are triangles. This is

$\frac{1}{5} \times 100 \% = \frac{100}{5} \% = 20 \%$

of the figures.

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Example Question #164 : Percentage

Assorted 1

What percent of the above figures have been shaded in?

Possible Answers:

$44 \frac{4}{9} \%$

$46 \frac{2}{3} \%$

$50 \%$

$40 \%$

Correct answer:

$46 \frac{2}{3} \%$

Explanation:

Of the fifteen figures, seven have been shaded in - $\frac{7}{15 }$ of the figures, or

$\frac{7}{15 } \times 100 \% = \frac{700}{15} \% = \frac{140}{3} \%$

$140 \div 3 = 46 \textrm{ R }2$ , so this is $46 \frac{2}{3} \%$ .

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Example Question #163 : Percentage

Para

The above parallelogram has been divided into triangles of equal size. What percent of the parallelogram has been shaded in?

Possible Answers:

$72 \%$

$66 \%$

$75 \%$

$80 \%$

Correct answer:

$75 \%$

Explanation:

18 of 24 triangles have been shaded in; this is $\frac{18}{24} = \frac{3}{4}$ of the parallelogram, which is equal to

$\frac{3}{4} \cdot 100 \% = \frac{300}{4} \% = 75 \%$

of the parallelogram.

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Example Question #166 : Percentage

is 25% of .

is 125% of .

is what percent of ?

Possible Answers:

$100 \%$

$500 \%$

$150 \%$

$20 \%$

Correct answer:

$500 \%$

Explanation:

Assume X = 100 ; this reasoning is independent of the actual value.

is 25% of , or, equivalently, $Y = \frac{25}{100} X = \frac{1}{4} X$ .

is 125% of , or, equivalently, $Z = \frac{125}{100} X = \frac{5}{4} X$ .

To determine what percent is of , evaluate:

$\frac{Z}{Y} \cdot 100 \%$

$= \frac{ \frac{5}{4} X}{ \frac{1}{4} X} \cdot 100 \%$

$= \frac{ \frac{5}{4} }{ \frac{1}{4} } \cdot 100 \%$

$= \frac{ 5}{1} \cdot 100 \%$

$= 5 \cdot 100 \%$

$= 500 \%$

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Example Question #166 : Percentage

is 30% of .

is $33 \frac{1}{3} \%$ of .

is what percent of ?

Possible Answers:

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

$90 \%$

$111 \frac{1}{9} \%$

$63 \frac{1}{3} \%$

Correct answer:

$90 \%$

Explanation:

30% of a number is equal to $\frac{30}{100} = \frac{30 \div 10}{100 \div 10 } = \frac{3}{10}$ of that number.

Therefore,

$A = \frac{3}{10} B$ , and

$\frac{10}{3} \cdot \frac{3}{10} B= \frac{10}{3} \cdot A$

$B= \frac{10}{3} A$

$33 \frac{1}{3} \%$ of a number is equal to $33 \frac{1}{3} \div 100 = \frac{100}{3} \times \frac {1}{100} = \frac{1}{3}$ of the number, so

$A = \frac{1}{3} C$

$3 \cdot \frac{1}{3} C = 3\cdot A$

C = 3A

To determine what percent is of , evaluate:

$\frac{C}{B} \cdot 100 \%$

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

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

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

$= \frac{900} {10} \%$

$= 90 \%$

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Example Question #167 : Percentage

is $\frac{1}{3} \%$ of .

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

is what percent of ?

Possible Answers:

$150 \%$

$6 \%$

$\frac{1}{6} \%$

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

Correct answer:

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

Explanation:

This reasoning is independent of the value of , so for simplicity's sake, we will assume that B = 600 ; the reason for this selection will be apparent later.

is $\frac{1}{3} \%$ of , or

$\frac{1}{3} \div 100 = \frac{1}{3} \times \frac{1}{100}= \frac{1}{300}$ of ; this is

$A = \frac{1}{300} B$

Similarly,

is $\frac{1}{2} \%$ of , or

$\frac{1}{2} \div 100 = \frac{1}{2} \times \frac{1}{100}= \frac{1}{200}$ of ; this is

$C = \frac{1}{200} B$ .

To determine what percent is of , evaluate:

$\frac{A}{C} \cdot 100 \%$

$= \frac{ \frac{1}{300} B}{ \frac{1}{200} B} \cdot 100 \%$

$= \frac{ \frac{1}{300} }{ \frac{1}{200} } \cdot 100 \%$

$= \frac{1}{300} \cdot 200 \cdot 100 \%$

$= \frac{20,000}{300} \%$

$= \frac{2 00}{3} \%$

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

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Example Question #164 : Percentage

A sweater that usually costs $\$60$ is on sale for $25\%$ off. How much does the sweater cost during the sale?

Possible Answers:

$\$75$

$\$45$

$\$15$

$\$11$

None of these

Correct answer:

$\$45$

Explanation:

To find the discounted amount, convert the percent to a decimal and multiply it by the original cost.

$25\%=0.25$

$\$60*0.25=\$15$

Then, subtract the discount amount from the original cost.

$\$60-\$15=\$45$

Answer: $\$45$

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

Pie_graph

Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?

Possible Answers:

27,472

26,557

39,835

37,938

16,259

Correct answer:

26,557

Explanation:

40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:

$\frac{60}{100} = \frac{15,934}{N}$

$60 N = 100 \cdot 15,934$

60 N = 1,593,400

$60 N \div 60= 1,593,400 \div 60$

N= 26,556.7

which rounds to 26,557 voters.

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ISEE Middle Level Math : Percentage

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #161 : Percentage

Example Question #162 : Percentage

Example Question #162 : Percentage

Example Question #164 : Percentage

Example Question #163 : Percentage

Example Question #166 : Percentage

Example Question #166 : Percentage

Example Question #167 : Percentage

Example Question #164 : Percentage

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

All ISEE Middle Level Math Resources

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