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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #601 : Concepts

30% of is equal to 40% of what number?

Possible Answers:

12 N

$\frac{3}{4}N$

$\frac{1}{12}N$

$\frac{4}{3}N$

Correct answer:

$\frac{3}{4}N$

Explanation:

30% of is equal to $\frac{30}{100} N = \frac{3}{10}N$ . Divide by 40%, or $\frac{40}{100} = \frac{4}{10}$ , to get

$\frac{3}{10}N \div \frac{4}{10} = \frac{3}{10}N \cdot \frac{10} {4} = \frac{3}{4}N$

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Example Question #602 : Concepts

percent of 1,000 is equal to what percent of 5,000?

Possible Answers:

20N

$\frac{1}{20}N$

$\frac{1}{5}N$

Correct answer:

$\frac{1}{5}N$

Explanation:

percent of 1,000 is equal to

$\frac{N}{100} \cdot 1,000 = 10 N$

This is

$\frac{10N}{5,000} \cdot 100 = \frac{1,000N}{5,000} = \frac{1}{5}N$

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Example Question #603 : Concepts

0.5 is what percent of 0.001 ?

Possible Answers:

$0.002 \%$

$0.2 \%$

$50,000 \%$

$5 00 \%$

Correct answer:

$50,000 \%$

Explanation:

To find what percent 0.5 is of 0.001, evaluate:

$\frac{0.5}{0.001} \times 100 \%$

$= \frac{0.5 \times 100}{0.001} \%$

$= \frac{50}{0.001} \%$

$= 50,000 \%$

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Example Question #12 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

is 30% of ; is 42% of .

is what percent of ?

Possible Answers:

$40 \%$

$71 \frac{3}{7} \%$

$140 \%$

$28 \frac{4}{7} \%$

Correct answer:

$140 \%$

Explanation:

We can choose a specific value for ; the reasoning is independent of this value.

Assume C = 100 . Then

$A = 100 \cdot 30 \% = 100 \cdot \frac{30}{100} = 30$

and

$B = 100 \cdot 42 \% = 100 \cdot \frac{42}{100} = 42$

To find out what percent is of , calculate:

$\frac{B}{A} \times 100 \% = \frac{42}{30} \times 100 \% = 140 \%$

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Example Question #604 : Arithmetic

is 40% of , which is 60% of . What percent of is ?

Possible Answers:

$416 \frac{2}{3} \%$

$24 \%$

$150 \%$

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

Correct answer:

$416 \frac{2}{3} \%$

Explanation:

This reasoning is independent of the value of , so choose C = 100 for simplicity's sake.

is 60% of C = 100 , which is 60. is 40% of this, or

$A = 60 \times 40 \% = 60 \times \frac{40 }{100} = 24$ .

To determine what percent is of , calculate:

$\frac{C}{A} \cdot 100 \% = \frac{100}{24} \cdot 100 \% = 416 \frac{2}{3} \%$

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Example Question #81 : Percentages

is four-fifths of , which is three-fifths of . By what percent must be increased to get ?

Possible Answers:

$108 \frac{1}{3} \%$

$48 \%$

$208 \frac{1}{3} \%$

$148 \%$

Correct answer:

$108 \frac{1}{3} \%$

Explanation:

This reasoning is independent of the value of , so, for simplicity's sake, we will set C = 100 .

is three-fifths of , so $B = \frac{3}{5}C = \frac{3}{5} \cdot 100 = 60$ .

is four-fifths of , so $A= \frac{4}{5}B = \frac{4}{5} \cdot 60 = 48$ .

To find out by what percent must be increased to yield , we calculate:

$\frac{C-A }{A} \times 100 \% = \frac{100-48 }{48} \times 100 \% = \frac{52}{48} \times 100 \% = 108 \frac{1}{3} \%$

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Example Question #604 : Arithmetic

20 is $\frac{1}{2}$ % of what number?

Possible Answers:

$\frac{2}{5}$

1,000

4,000

$\frac{1}{10}$

Correct answer:

4,000

Explanation:

Let be the number in question. If 20 is $\frac{1}{2}$ % of , then

$\frac{\frac{1}{2} }{100}\cdot N = 20$

$\frac{\frac{1}{2} }{100}\cdot N \cdot 100= 20 \cdot 100$

$\frac{1}{2} \cdot N = 2,0 00$

$\frac{1}{2} \cdot N \cdot 2 = 2,0 00 \cdot 2$

N = 4,000

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Example Question #81 : Percentages

Four students ran for student body president - Anya, Florida, Moesha, and Winston.

According to the rules, a candidate must win more than 50% of the vote in order to claim an outright victory; otherwise, a runoff must be held between the top two vote-getters. It is known that Florida won 67 votes, Moesha won 91 votes, and Winston won 180 votes. It is also known that there will be a runoff. At the very least, what percent of the vote did Anya win? (Nearest whole percent)

Possible Answers:

$21 \%$

$7 \%$

$6 \%$

$12 \%$

Correct answer:

$6 \%$

Explanation:

Neither Florida nor Moesha won the most votes, so either Winston or Anya did. If there is going to be a runoff, then regardless of the outcome, the total of the votes won by Winston's opponents must at least equal the votes won by Winston. If we let stand for the number of votes Anya won, then

$A + 67 + 91 \geq 180$

$A + 158 \geq180$

$A + 158 - 158 \geq180 - 158$

$A \geq 22$

At the very least, Anya must have won 22 votes, which in this scenario would have been equal to:

$\frac{22}{22 + 67 + 91 +180} \times 100 \%$

$= \frac{22}{360} \times 100 \%$

$\approx 6.1 \%$

This makes 6% the best choice.

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Example Question #171 : Grade 7

If you get a 25% discount, what percentage of the original price will you have to pay?

Possible Answers:

$80\%$

$100\%$

$75\%$

$25\%$

Correct answer:

$75\%$

Explanation:

The original price will represent 100% of the item price since that represents the whole for the problem.

If you get 25% off, you must take that away from the 100%.

100-25=75

so you will have to pay 75% of the original price.

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Example Question #604 : Concepts

What is the sale price of a product that costs $\$500$ if the sale is $40\%$ off the original price?

Possible Answers:

$\$700$

$\$800$

$\$300$

$\$540$

$\$200$

Correct answer:

$\$300$

Explanation:

First, find $40\%$ of $\$500$ :

$0.4\cdot \$500=\$200$

Then, subtract this value from the whole:

$\$500-\$200=\$300$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #601 : Concepts

Example Question #602 : Concepts

Example Question #603 : Concepts

Example Question #12 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

Example Question #604 : Arithmetic

Example Question #81 : Percentages

Example Question #604 : Arithmetic

Example Question #81 : Percentages

Example Question #171 : Grade 7

Example Question #604 : Concepts

All HSPT Math Resources

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