HSPT Quantitative : Non-Geometric Comparison

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #11 : Non Geometric Comparison

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

a) \displaystyle 11^{2}

b) The smallest prime number larger than \displaystyle 100

c) \displaystyle 95 percent of \displaystyle 120

Possible Answers:

\displaystyle b>c>a

\displaystyle b< c< a

\displaystyle a< b< c

\displaystyle a=b< c

Correct answer:

\displaystyle b< c< a

Explanation:

a) \displaystyle 11^{2} \displaystyle = 11\cdot11=121

b) The smallest prime number larger than \displaystyle 100 is \displaystyle 101.

c) \displaystyle 95 percent of \displaystyle 120

 \displaystyle 120\cdot.95=114

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

 

Example Question #11 : Non Geometric Comparison

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

a) \displaystyle (2+7)\cdot8

b) \displaystyle 2+(7\cdot8)

c) \displaystyle (2\cdot8)+7

 

Possible Answers:

\displaystyle b< a< c

\displaystyle b< c< a

\displaystyle a< b< c

\displaystyle a>b>c

Correct answer:

\displaystyle a>b>c

Explanation:

Always do the operations in parantheses first, then multiplication, then addition.

a) \displaystyle (2+7)\cdot8 = 9\cdot8 = 72

b) \displaystyle 2+(7\cdot8) = 2+56 =58

c) \displaystyle (2\cdot8)+7 = 16+7 = 23

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

 

Example Question #12 : Non Geometric Comparison

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

a) \displaystyle \frac{2}{3} of \displaystyle 36

b) \displaystyle \frac{5}{2} of \displaystyle 36

c) \displaystyle \frac{5}{6} of \displaystyle 72

 

Possible Answers:

\displaystyle a=b=c

\displaystyle a< c< b

\displaystyle a=c< b

\displaystyle b< c< a

Correct answer:

\displaystyle a< c< b

Explanation:

Multiply each fraction by the number to find each value:

a) \displaystyle \frac{2}{3} of \displaystyle 36

\displaystyle \frac{36\cdot2}{3}=24

b) \displaystyle \frac{5}{2} of \displaystyle 36

\displaystyle \frac{36\cdot5}{2}=90

c) \displaystyle \frac{5}{6} of \displaystyle 72

\displaystyle \frac{72\cdot5}{6}=60

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

Example Question #12 : How To Make Non Geometric Comparisons

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

a) \displaystyle 6+(2\cdot3)

b) \displaystyle (6+2)\cdot3

c) \displaystyle (6+3)^2

Possible Answers:

(a) is greater than (b) and (c).

(c) is greater than (a) and (b).

(a) and (b) are equal.

(a), (b), and (c) are all equal.

Correct answer:

(c) is greater than (a) and (b).

Explanation:

Always do the operations in parantheses first, then exponents, multiplication, and last addition.

a) \displaystyle 6+(2\cdot3) \displaystyle =6+6=12

b) \displaystyle (6+2)\cdot3 \displaystyle =8\cdot3=24

c) \displaystyle (6+3)^2 \displaystyle = 9^2 = 81

Example Question #13 : How To Make Non Geometric Comparisons

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

a) \displaystyle .6 \cdot .4

b) \displaystyle .6 \cdot4

c) \displaystyle 6 \cdot .4

Possible Answers:

(a), (b), and (c) are equal.

(b) is greater than both (a) and (c).

(b) and (c) are equal.

(a) is greater than both (b) and (c).

Correct answer:

(b) and (c) are equal.

Explanation:

Compute each value in order to compare them:

a) \displaystyle .6 \cdot .4 \displaystyle =.24

b) \displaystyle .6 \cdot4 \displaystyle =2.4

c) \displaystyle 6 \cdot .4 \displaystyle =2.4

Therefore (b) and (c) are equal, and they are greater than (a).

Example Question #12 : Non Geometric Comparison

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

a) \displaystyle \frac{1}{5}

b) \displaystyle \frac{3}{10}

c) \displaystyle \frac{1}{10}

 

Possible Answers:

(c) is greater than (a) or (b).

(b) is greater than (a) or (c).

(a) and (b) are equal.

(a), (b), and (c) are all equal.

Correct answer:

(b) is greater than (a) or (c).

Explanation:

Rewrite the first fraction with a denominator of \displaystyle 10 in order to compare more easily:

a) \displaystyle \frac{1}{5}=\frac{2}{10}

b) \displaystyle \frac{3}{10}

c) \displaystyle \frac{1}{10}

 

It becomes clear that (b) is the greatest, followed by (a), then (c).

Example Question #14 : Non Geometric Comparison

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

a) \displaystyle 30 percent of \displaystyle 100

b) \displaystyle 60 percent of \displaystyle 50

c) \displaystyle 60 percent of \displaystyle 200

Possible Answers:

(b) is greater than (a) or (c).

(a) and (c) are equal.

(a) is greater than (b) or (c).

(a) and (b) are equal.

Correct answer:

(a) and (b) are equal.

Explanation:

Calculate the percents in order to compare them:

a) \displaystyle 30 percent of \displaystyle 100

\displaystyle 100\cdot.30=30

b) \displaystyle 60 percent of \displaystyle 50

\displaystyle 50\cdot.60=30

c) \displaystyle 60 percent of \displaystyle 200

\displaystyle 200\cdot.60=120

Therefore (a) and (b) are equal, and less than (c).

Example Question #15 : Non Geometric Comparison

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

a) \displaystyle 2^5

b)\displaystyle 3^3

c)\displaystyle 4^2

Possible Answers:

\displaystyle a< b< c

\displaystyle a=b=c

\displaystyle a=b>c

\displaystyle a>b>c

Correct answer:

\displaystyle a>b>c

Explanation:

Calculate the exponents to compare the values:

a) \displaystyle 2^5 \displaystyle =2\cdot2\cdot2\cdot2\cdot2=32

b) \displaystyle 3^3 \displaystyle =3\cdot3\cdot3=27

c) \displaystyle 4^2 \displaystyle =4\cdot4=16

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

 

Example Question #13 : Non Geometric Comparison

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

a) \displaystyle 7x

b) \displaystyle 2(x+5x)

c) \displaystyle 2x+5x

 

Possible Answers:

Only (a) and (c) are equal.

Only (b) and (c) are equal.

(a), (b), and (c) are all equal.

None are equal.

Correct answer:

Only (a) and (c) are equal.

Explanation:

Simplify each expression to see if they are equal:

a) \displaystyle 7x (already simplified)

b) \displaystyle 2(x+5x) \displaystyle =2x+10x=12x

c) \displaystyle 2x+5x \displaystyle =7x

Therefore (a) and (c) are equal, but (b) is different.

 

Example Question #14 : Non Geometric Comparison

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

a) \displaystyle \frac{2}{3}

b) \displaystyle 60 percent

c) \displaystyle .65

Possible Answers:

(a) is greater than (b) and (c).

(b) is greater than (a) and (c).

(a), (b), and (c) are all equal.

(c) is greater than (a) and (b).

Correct answer:

(a) is greater than (b) and (c).

Explanation:

Convert each expression into a decimal in order to compare them:

a) \displaystyle .\bar{66}

b) \displaystyle .6

c)\displaystyle .65

Therefore (a) is the largest.

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