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HSPT Math : Percentages

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Example Question #171 : Ratios & Proportional Relationships

is 30% of ; is 42% of .

is what percent of ?

Possible Answers:

$40 \%$

$140 \%$

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

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

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 #1195 : Hspt Mathematics

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

Possible Answers:

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

$150 \%$

$24 \%$

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

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 #606 : Arithmetic

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

Possible Answers:

$48 \%$

$148 \%$

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

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

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 #607 : Arithmetic

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

Possible Answers:

$\frac{2}{5}$

$\frac{1}{10}$

4,000

1,000

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 #1201 : Hspt Mathematics

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:

$7 \%$

$12 \%$

$6 \%$

$21 \%$

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 #601 : Arithmetic

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

Possible Answers:

$25\%$

$75\%$

$80\%$

$100\%$

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 #602 : Arithmetic

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

Possible Answers:

$\$300$

$\$700$

$\$540$

$\$200$

$\$800$

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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Example Question #171 : Ratios & Proportional Relationships

What is the sale price of a television if it is on sale for % off the original price of $\$175.00?$

Possible Answers:

$\$52.50$

$\$50.00$

$\$125.00$

$\$75.00$

$\$122.50$

Correct answer:

$\$52.50$

Explanation:

First, multiply:

$175.00\ast .70=122.50$

Then subtract that amount from the original price:

175.00-122.50=52.50

Answer: The sale price is $\$52.50$ .

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Example Question #81 : Percentages

24 is what percent of 96?

Possible Answers:

$15\%$

$45\%$

$25\%$

$33\%$

Correct answer:

$25\%$

Explanation:

Translate the sentence into an equation

24=x(96)

Isolate and you get .

Remember that the question is asking for a percentage, so convert into $25\%$ .

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HSPT Math : Percentages

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #171 : Ratios & Proportional Relationships

Example Question #1195 : Hspt Mathematics

Example Question #606 : Arithmetic

Example Question #607 : Arithmetic

Example Question #1201 : Hspt Mathematics

Example Question #601 : Arithmetic

Example Question #602 : Arithmetic

Example Question #171 : Ratios & Proportional Relationships

Example Question #81 : Percentages

All HSPT Math Resources

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