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HSPT Quantitative : HSPT Quantitative Skills

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Example Questions

Example Question #131 : Hspt Quantitative Skills

Examine a, b, and c and find the best answer.

a. percent of

b. percent of

c. percent of

Possible Answers:

a>b=c

a>b>c

a=b<c

a=b=c

a<b=c

Correct answer:

a=b<c

Explanation:

Find the values of a, b, and c.

$a=\tfrac{20}{100}*50=\tfrac{1000}{100}=10$

$b=\tfrac{50}{100}*20=\tfrac{1000}{100}=10$

$c=\tfrac{30}{100}*90=\tfrac{2700}{100}=27$

With these values, a=b<c .

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Example Question #131 : Hspt Quantitative Skills

Examine (a), (b), and (c) to find the best answer:

a) $\frac{3}{4}$ of

b) $\frac{4}{8}$ of

c) $\frac{8}{3}$ of

Possible Answers:

b<a<c

b>a>c

a>b>c

a=b=c

Correct answer:

b<a<c

Explanation:

Calculate the expressions to compare the values:

a) $\frac{3}{}4$ of $=\frac{3\cdot8}{4}=6$

b) $\frac{4}{8}$ of $=\frac{4\cdot3}{8}=1\frac{1}{2}$

c) $\frac{8}{3}$ of $= \frac{8\cdot4}{3}=10\frac{2}{3}$

Therefore (b) is smaller than (a), which is smaller than (c).

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Example Question #92 : How To Make Non Geometric Comparisons

is 30% of 12.

is 40% of 9.

is 50% of 6.

Which of the following is correct?

Possible Answers:

A = B

C> A

C = B

A > B

Correct answer:

A = B

Explanation:

is 30% of 12, and the decimal equivalent of 30% is 0.3. Therefore,

$A = 12 \times 0.3 = 3.6$

is 40% of 9, and the decimal equivalent of 40% is 0.4. Therefore,

$B = 9 \times 0.4 = 3.6$

is 50% of 6, and the decimal equivalent of 40% is 0.4. Therefore,

$C = 6 \times 0.5 = 3$

Therefore, C< A = B .

Of the four choices, only A = B is a correct statement.

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Example Question #133 : Hspt Quantitative Skills

$A = \frac{1}{3} + \frac{1}{6}$

$B = \frac{1}{3} \times \frac{1}{2}$

$C = \frac{1}{3} \div \frac{1}{2}$

Which of the following is correct?

Possible Answers:

B =A

B> A

A> C

A< C

Correct answer:

A< C

Explanation:

$A = \frac{1}{3} + \frac{1}{6}$

To add two fractions, first express them in terms of the same denominator; the least common denominator of 3 and 6 is 6, so multiply both halves of the first fraction by 2:

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

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

Add the numerators and preserve the common denominator:

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

$A = \frac{ 3}{6}$

Reduce by dividing both halves by their greatest common factor, 3:

$A = \frac{ 3 \div 3 }{6 \div 3}$

$A = \frac{1 }{2}$

$B = \frac{1}{3} \times \frac{1}{2}$

To multiply two fractions, multiply numerators and multiply denominators:

$B = \frac{1 \times 1}{3 \times 2}$

$B = \frac{1 }{6}$

$C = \frac{1}{3} \div \frac{1}{2}$

To divide two fractions, multiply the first number by the reciprocal of the second number - switch the two halves of the latter:

$C = \frac{1}{3} \times \frac{2} {1}$

Again, multiply numerators and multiply denominators:

$C = \frac{1 \times 2 }{3 \times 1}$

$C = \frac{ 2 }{3 }$

Compare the fractions by expressing them in terms of the same denominator. The least common multiple of 2, 3, and 6 is 6; rewrite each fraction by multiplying whatever number yields this common denominator:

$A = \frac{1 }{2} = \frac{1 \times 3 }{2 \times 3} =\frac{3}{6 }$

$B = \frac{1 }{6}$

$C = \frac{ 2 \times 2}{3 \times 2 }= \frac{4}{6}$

Compare fractions with the same denominator by comparing numerators:

1< 3< 4 , so

$\frac{1 }{6} < \frac{3}{6 } < \frac{4}{6 }$ , and

B <A< C .

Of the four choices, only A< C is a correct statement.

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Example Question #134 : Hspt Quantitative Skills

is ten added to the square of ten.

is twenty added to the square of nine.

is thirty added to the square of eight.

Which of the following is correct?

Possible Answers:

A > C

B < C

A = C

B = C

Correct answer:

A > C

Explanation:

is ten added to the square of ten - that is,

$A = 10^{2}+ 10$

Evaluate this according to the order of operations by squaring, then by adding.

$A = 10^{2}+ 10 = 100 + 10 = 110$

Evaluate the other two expressions using the same order:

is twenty added to the square of nine, so

$B = 9^{2}+ 20 = 81 + 20 = 101$

is thirty added to the square of eight, so

$C = 8^{2}+ 30 = 64 + 30 = 94$

A > B > C , so the only correct statement of the four is A > C .

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Example Question #93 : How To Make Non Geometric Comparisons

$A = 12+ 12 \times 12$

$B = 12 \times 12 - 12$

$C = 12 \times 12 + 12$

Which of the following is correct?

Possible Answers:

C> A

C< A

B < C

B =C

Correct answer:

B < C

Explanation:

By the order of operations, multiplication precedes either addition or subtraction, so calculate accordingly:

$A = 12+ 12 \times 12 =12+ 144 = 156$

$B = 12 \times 12 - 12 = 144 - 12 = 132$

$C = 12 \times 12 + 12 = 144 + 12 = 156$

B < A = C ,

so the only correct statement among the choices is B < C .

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Example Question #134 : Hspt Quantitative Skills

$A = 200 \times 3 \times 0.04$

$B = 300 \times 4 \times 0.02$

$C = 400 \times 2 \times 0.03$

Which is a true statement?

Possible Answers:

A = C < B

A = B < C

B= C < A

A = B = C

Correct answer:

A = B = C

Explanation:

$A = 200 \times 3 \times 0.04= 600 \times 0.04 = 24$

$B = 300 \times 4 \times 0.02 = 1,200 \times 0.02 = 24$

$C = 400 \times 2 \times 0.03 = 800 \times 0.03 = 24$

A = B = C .

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Example Question #137 : Hspt Quantitative Skills

$A = 25 + 25 \div 10 \cdot 5$

$B = 25 \cdot 5 + 25 \div 10$

$C = 25 + 25 \cdot 5 \div 10$

Which of the following is correct?

Possible Answers:

A= B

C = B

A < B

C > B

Correct answer:

A < B

Explanation:

Each expression can be calculated according to the order of operations: Multiplication and division in left to right order, then addition and subtraction in left to right order.

$A = 25 + 25 \div 10 \cdot 5$

Divide first:

$A = 25 + 2.5 \cdot 5$

Multiply second:

A = 25 +12.5

Add last:

A = 37.5

$B = 25 \cdot 5 + 25 \div 10$

Multiply first:

$B = 125 + 25 \div 10$

Divide second:

B = 125 + 2.5

Add last:

B = 127.5

$C = 25 + 25 \cdot 5 \div 10$

Multiply first:

$C = 25 + 125 \div 10$

Divide second:

C = 25 + 12.5

Add last:

C = 37.5

A= C < B

The only correct statement among the choices is A < B .

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Example Question #135 : Hspt Quantitative Skills

is 30% of 40.

is 20% of 60.

is 10% of 80.

Which of the following is correct?

Possible Answers:

A > B

C = B

C> B

A = B

Correct answer:

A = B

Explanation:

30% of a number is equal to that number multiplied by the decimal equivalent of 30%, which is 0.30, or 0.3:

is 30% of 40, so

$A = 0.3 \times 40 = 12$

Similarly,

is 20% of 60, so

$B = 0.20 \times 60 = 12$

is 10% of 80, so

$c=0.10 \times 80 = 8$

C < A = B .

The only correct statement of the four is A = B .

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Example Question #93 : How To Make Non Geometric Comparisons

x = 4, y = 8, z= 5

A = xy - z

B = xz -y

C= yz-x

Which of the following is correct?

Possible Answers:

C< B

A < C

A = B

B> A

Correct answer:

A < C

Explanation:

In each expression, substitute, then evaluate. Follow the order of operations, which dictates that multiplication precedes subtraction:

$A = xy - z = 4 \times 8 - 5 = 32 - 5 = 27$

$B = xz -y = 4 \times 5 - 8 = 20- 8 = 12$

$C= yz-x = 8 \times 5 - 4 = 40 - 4 = 36$

C > A > B

The only correct choice is A < C .

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All HSPT Quantitative Resources

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HSPT Quantitative : HSPT Quantitative Skills

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #131 : Hspt Quantitative Skills

Example Question #131 : Hspt Quantitative Skills

Example Question #92 : How To Make Non Geometric Comparisons

Example Question #133 : Hspt Quantitative Skills

Example Question #134 : Hspt Quantitative Skills

Example Question #93 : How To Make Non Geometric Comparisons

Example Question #134 : Hspt Quantitative Skills

Example Question #137 : Hspt Quantitative Skills

Example Question #135 : Hspt Quantitative Skills

Example Question #93 : How To Make Non Geometric Comparisons

All HSPT Quantitative Resources

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