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HSPT Quantitative : Number Manipulation*

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #201 : Number Manipulation*

A number divided by the sum of 25 and 7 is equal to $1\frac{1}{2}$ . What is that number?

Possible Answers:

$\frac{3}{64}$

$32\frac{1}{2}$

Correct answer:

Explanation:

The sum of 25 and 7 is 25+7= 32 , so "a number divided by the sum of 25 and 7 is equal to $1\frac{1}{2}$ ." can be restated as "a number divided by 32 is equal to $1\frac{1}{2}$ . ". This can be rewritten as

$x \div 32 = 1 \frac{1}{2}$ ,

which can be solved by multiplying both sides by 32, thereby isolating :

$x \div 32 \cdot 32 = 1 \frac{1}{2} \cdot 32$

$x = 1 \frac{1}{2} \cdot 32$

Rewrite as improper fractions and multiply across, then reduce:

$x = \frac{3}{2} \cdot \frac{32}{1} = \frac{96}{2} = 48$

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Example Question #201 : Number Manipulation*

Which of the following is not equal to 30?

(a) 20% of 150

(b) $\frac{1}{5}$ of 150

Possible Answers:

(b)

(a)

(c)

All three expressions are equal to 30.

Correct answer:

(c)

Explanation:

(a) 20% of 150 is equal to the decimal equivalent of 20%, which is 0.20, multiplied by 150:

$0.20 \times 150 = 30$

(b) $\frac{1}{5}$ of 150 can be calculated as follows:

$\frac{1}{5} \times 150 = \frac{1}{5} \times \frac{150}{1} = \frac{150}{5} = 30$

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Example Question #203 : Number Manipulation*

What number increased by 15% is equal to 230?

Possible Answers:

$210 \frac{1}{2}$

215

200

$195\frac{1}{2}$

Correct answer:

200

Explanation:

If is the number in question, then 15% of the number is

$\frac{15}{100} N$

Increasing a number by 15% is equivalent to adding $\frac{15}{100} N$ to ; since this is equal to 230, this sets up the equation

$N + \frac{15}{100} N = 230$

Collect like terms:

$\frac{100}{100}N + \frac{15}{100} N = 230$

$\frac{1 15}{100} N = 230$

Multiply both sides by $\frac{100} {1 15}$ :

$\frac{100} {1 15} \cdot \frac{1 15}{100} N = \frac{100} {1 15} \cdot230$

$N = \frac{100} {1 15} \cdot \frac{230}{1}= \frac{23,000} {1 15} = 200$ .

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Example Question #202 : Number Manipulation*

Subtract the square root of 144 from the square of 144.

Possible Answers:

20,748

20,724

276

300

Correct answer:

20,724

Explanation:

Since $12^{2} = 12 \times 12 = 144$ , the square root of 144 is 12 (there are actually two square roots, 12 and , but "the" square root refers to the positive root).

The square of 144 is

$144 ^{2} = 144\times 144 = 20,736$

Subtract 12 from 20,736:

20,736 - 12 = 20,724

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Example Question #203 : Number Manipulation*

Add the square root of 36 to the square of 6.

Possible Answers:

Correct answer:

Explanation:

$6^{2} = 6 \times 6 = 36$ ; therefore, the square of 6 is 36, and the square root of 36 is 6 (36 actually two square roots, 6 and , but "the" square root refers to its positive square root). Adding the square root of 36 to the square of 6 is the same as adding 6 to 36, so add:

36+6 = 42 .

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Example Question #554 : Hspt Quantitative Skills

20% of a number is equal to the square root of 36. What is the number?

Possible Answers:

6,480

$1\frac{1}{5}$

720

Correct answer:

Explanation:

If is the number in question, "20% of a number" can be written as $\frac{20}{100}N$ , or, in lowest terms, $\frac{1}{5}N$ .

Also, since $6^{2} = 6 \times 6 = 36$ , 36 has 6 as its square root (there are actually two square roots, 6 and , but "the" square root refers to the positive root). Therefore, "20% of a number is equal to the square root of 36" can be reworded as "20% of a number is equal to 6", and written as the equation

$\frac{1}{5}N = 6$

Multiply both sides by 5:

$5 \cdot \frac{1}{5}N = 5 \cdot 6$

N = 30

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Example Question #207 : Number Manipulation*

Two thirds of a number is equal to two times forty. What is that number?

Possible Answers:

$13\frac{1}{3}$

$53\frac{1}{3}$

120

Correct answer:

120

Explanation:

Let be the number in question. "Two thirds of a number is equal to two times forty" translates as the equation

$\frac{2}{3} x = 2 \cdot 40$

Multiply on the right:

$\frac{2}{3} x = 80$

Multiply both sides by $\frac{3}{2}$ to isolate :

$\frac{3}{2} \cdot \frac{2}{3} x =\frac{3}{2} \cdot 80$

x =120

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Example Question #208 : Number Manipulation*

Add one fourth of 26 to one third of 33. What is the result?

Possible Answers:

$17 \frac{1}{2}$

203

105

$105\frac{1}{2}$

Correct answer:

$17 \frac{1}{2}$

Explanation:

"Add[ing] one fourth of 26 to one third of 33" means to evaluate the expression

$\frac{1}{4} \times 26 + \frac{1}{3} \times 33$

By the order of operations, perform the leftmost multiplication first:

$\frac{1}{4} \times \frac{26 }{1}+ \frac{1}{3} \times 33$

$= \frac{26 }{4}+ \frac{1}{3} \times 33$

$= \frac{13}{2}+ \frac{1}{3} \times 33$

$=6 \frac{1}{2}+ \frac{1}{3} \times 33$

Perform the rightmost multiplication next:

$=6 \frac{1}{2}+ \frac{1}{3} \times \frac{33}{1}$

$=6 \frac{1}{2}+ \frac{33}{3}$

$=6 \frac{1}{2}+ 11$

Now add:

$6 \frac{1}{2}+ 11=17 \frac{1}{2}$

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Example Question #209 : Number Manipulation*

Ten times a number is twenty more than six times that same number. What is the number?

Possible Answers:

$2\frac{3}{5}$

$1\frac{1}{4}$

Correct answer:

Explanation:

Letting the unknown number, "ten times a number is twenty more than six times that same number" can be written as the algebraic equation

10 x = 6x + 20

Subtract from both sides:

10 x - 6x = 6x + 20 - 6x

Collect like terms:

4x= 20

Divide both sides by 4, thereby isolating the :

$\frac{4x}{4}= \frac{20}{4}$

x = 5

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Example Question #561 : Hspt Quantitative Skills

Evaluate:

30% of $\frac{7}{10}$

Possible Answers:

$\frac{21}{100}$

$\frac{3}{7}$

$2\frac{1}{3}$

$4 \frac{16}{21}$

Correct answer:

$\frac{21}{100}$

Explanation:

30% of a number is equal to $\frac{30}{100}$ multiplied by that number. Reduce this by dividing both halves of the fraction by the greatest common factor of 30 and 100, which is 10:

$\frac{30}{100} = \frac{30 \times 10 }{100 \times 10 } = \frac{3}{10}$

Multiply this by $\frac{7}{10}$ by multiplying numerators and multiplying denominators:

$\frac{3}{10} \times \frac{7}{10} = \frac{3 \times 7}{10 \times 10} = \frac{21}{100}$ ,

the correct response.

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HSPT Quantitative : Number Manipulation*

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #201 : Number Manipulation*

Example Question #201 : Number Manipulation*

Example Question #203 : Number Manipulation*

Example Question #202 : Number Manipulation*

Example Question #203 : Number Manipulation*

Example Question #554 : Hspt Quantitative Skills

Example Question #207 : Number Manipulation*

Example Question #208 : Number Manipulation*

Example Question #209 : Number Manipulation*

Example Question #561 : Hspt Quantitative Skills

All HSPT Quantitative Resources

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