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HSPT Quantitative : How to manipulate numbers

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6 Diagnostic Tests 55 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #171 : How To Manipulate Numbers

$\displaystyle 14$ is what percentage of $\displaystyle 80$?

Possible Answers:

$5.71\%$ $\displaystyle 5.71\%$

$1.12\%$ $\displaystyle 1.12\%$

$17.5\%$ $\displaystyle 17.5\%$

$0.175\%$ $\displaystyle 0.175\%$

Correct answer:

$17.5\%$ $\displaystyle 17.5\%$

Explanation:

First, divide $\displaystyle 14$ by $\displaystyle 80$:

$14\div 80=0.175$ $\displaystyle 14\div 80=0.175$

Next, convert to a percentage by multiplying by 100 $\displaystyle 100$:

$0.175\cdot100=17.5\%$ $\displaystyle 0.175\cdot100=17.5\%$

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Example Question #172 : How To Manipulate Numbers

What is $45\%$ $\displaystyle 45\%$ of $\displaystyle 16$?

Possible Answers:

$\displaystyle 7$

7.2 $\displaystyle 7.2$

7.5 $\displaystyle 7.5$

$\displaystyle 8$

Correct answer:

7.2 $\displaystyle 7.2$

Explanation:

Multiply $\displaystyle 16$ by $45\%$ $\displaystyle 45\%$, or 0.45 $\displaystyle 0.45$:

$16\cdot0.45=7.2$ $\displaystyle 16\cdot0.45=7.2$

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Example Question #173 : How To Manipulate Numbers

What number, when divided by the product of $\displaystyle 16$ and 3.5 $\displaystyle 3.5$, equals the square root of $\displaystyle 9$?

Possible Answers:

58.5 $\displaystyle 58.5$

$\displaystyle 56$

$\displaystyle 18$

168 $\displaystyle 168$

Correct answer:

168 $\displaystyle 168$

Explanation:

Work backwards to solve this problem. First, the product of $\displaystyle 16$ and 3.5 $\displaystyle 3.5$ is 118 $\displaystyle 118$:

$16\cdot3.5=56$ $\displaystyle 16\cdot3.5=56$

Next, the square root of $\displaystyle 9$ is $\displaystyle 3$:

$\sqrt{9}=3$ $\displaystyle \sqrt{9}=3$

Now, the question is, "What number, when divided by $\displaystyle 56$, equals $\displaystyle 3$?" This can also be written as:

$\frac{x}{56}=3$ $\displaystyle \frac{x}{56}=3$

Multiply both sides by $\displaystyle 56$ to find $\displaystyle x$:

$x=56\cdot3=168$ $\displaystyle x=56\cdot3=168$

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Example Question #174 : How To Manipulate Numbers

What number added to 15 gives you $\dpi{100} \frac{1}{4}$ $\displaystyle \dpi{100} \frac{1}{4}$ of 72 ?

Possible Answers:

$\dpi{100} 3$ $\displaystyle \dpi{100} 3$

$\dpi{100} 6$ $\displaystyle \dpi{100} 6$

$\dpi{100} 4$ $\displaystyle \dpi{100} 4$

$\dpi{100} 12$ $\displaystyle \dpi{100} 12$

Correct answer:

$\dpi{100} 3$ $\displaystyle \dpi{100} 3$

Explanation:

Set up an equation using the information provided.

$\dpi{100} 15+x=\frac{1}{4}\cdot 72$ $\displaystyle \dpi{100} 15+x=\frac{1}{4}\cdot 72$

$\dpi{100} 15+x=18$ $\displaystyle \dpi{100} 15+x=18$

$\dpi{100} 15+x-15=18-15$ $\displaystyle \dpi{100} 15+x-15=18-15$

$\dpi{100} x=3$ $\displaystyle \dpi{100} x=3$

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Example Question #175 : How To Manipulate Numbers

$\displaystyle 60$ is $\displaystyle 5$ percent of what number?

Possible Answers:

1500 $\displaystyle 1500$

120 $\displaystyle 120$

150 $\displaystyle 150$

1200 $\displaystyle 1200$

Correct answer:

1200 $\displaystyle 1200$

Explanation:

Set up a proportion, representing the unknown number with $\displaystyle x$:

$\frac{60}{x}=\frac{5}{100}$ $\displaystyle \frac{60}{x}=\frac{5}{100}$

Then cross multiply and solve:

6000=5x $\displaystyle 6000=5x$

$x=\frac{6000}{5}=1200$ $\displaystyle x=\frac{6000}{5}=1200$

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Example Question #176 : How To Manipulate Numbers

What number, when divided by $\displaystyle 6$, is half the product of $\displaystyle 13$ and $\displaystyle 8$?

Possible Answers:

404 $\displaystyle 404$

298 $\displaystyle 298$

312 $\displaystyle 312$

415 $\displaystyle 415$

Correct answer:

312 $\displaystyle 312$

Explanation:

First find the product of $\displaystyle 13$ and $\displaystyle 8$:

$13\cdot8=104$ $\displaystyle 13\cdot8=104$

Then find half the product by dividing by 2:

$104\div2=52$ $\displaystyle 104\div2=52$

Now multiply by $\displaystyle 6$ to reverse the division:

$52\cdot6=312$ $\displaystyle 52\cdot6=312$

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Example Question #177 : How To Manipulate Numbers

What is $\displaystyle 16$ percent of $\displaystyle 64$?

Possible Answers:

12.05 $\displaystyle 12.05$

10.24 $\displaystyle 10.24$

$\displaystyle 4$

$\displaystyle 25$

Correct answer:

10.24 $\displaystyle 10.24$

Explanation:

Multipy $\displaystyle 64$ by the decimal version of the percentage:

$64\times .16=10.24$ $\displaystyle 64\times .16=10.24$

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Example Question #178 : How To Manipulate Numbers

What is $\displaystyle 6$ percent of 106 $\displaystyle 106$?

Possible Answers:

7.3 $\displaystyle 7.3$

$\displaystyle 7$

$6.\overline{66}$ $\displaystyle 6.\overline{66}$

6.36 $\displaystyle 6.36$

Correct answer:

6.36 $\displaystyle 6.36$

Explanation:

Multiply the number by the decimal version of the percentage:

$106\times .06=6.36$ $\displaystyle 106\times .06=6.36$

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Example Question #179 : How To Manipulate Numbers

What is $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of $\displaystyle 13$ less than $\displaystyle 93$?

Possible Answers:

$\displaystyle 48$

$\displaystyle 55$

$\displaystyle 60$

$\displaystyle 80$

Correct answer:

$\displaystyle 60$

Explanation:

First, $\displaystyle 13$ less than $\displaystyle 93$ is:

$\displaystyle 93-13=80$

Next, find $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of that value:

$\frac{80\cdot3}4{}=60$ $\displaystyle \frac{80\cdot3}4{}=60$

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Example Question #180 : How To Manipulate Numbers

What number is 2 percent of 3/8 of 72?

Possible Answers:

5.42 $\displaystyle 5.42$

1.32 $\displaystyle 1.32$

2.45 $\displaystyle 2.45$

0.54 $\displaystyle 0.54$

0.75 $\displaystyle 0.75$

Correct answer:

0.54 $\displaystyle 0.54$

Explanation:

First we need to find 3/8 of 72. To do this, convert 72 into a fraction and multiply.

$\frac{3}{8}\cdot \frac{72}{1} = \frac{216}{8}= 27$ $\displaystyle \frac{3}{8}\cdot \frac{72}{1} = \frac{216}{8}= 27$

To find 2 percent of 27, convert 2 percent into decimal form (0.02) and multiply it by 27.

$0.02 \cdot 27 = 0.54$ $\displaystyle 0.02 \cdot 27 = 0.54$

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HSPT Quantitative : How to manipulate numbers

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #171 : How To Manipulate Numbers

Example Question #172 : How To Manipulate Numbers

Example Question #173 : How To Manipulate Numbers

Example Question #174 : How To Manipulate Numbers

Example Question #175 : How To Manipulate Numbers

Example Question #176 : How To Manipulate Numbers

Example Question #177 : How To Manipulate Numbers

Example Question #178 : How To Manipulate Numbers

Example Question #179 : How To Manipulate Numbers

Example Question #180 : How To Manipulate Numbers

All HSPT Quantitative Resources

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