HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #41 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

When simplifying the expressions, follow the order of operations: parentheses, exponents, multiplication, then addition.

a)  

b)  

c)  =

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

Example Question #42 : Non Geometric Comparison

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

a)  percent of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

Calculate the expressions to compare the values:

a)   percent of  

b)   of 

c)   of 

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

Example Question #43 : Non Geometric Comparison

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

a)  of 

b)  of 

c)  of  

Possible Answers:

(a) is equal to (c)

(a) is equal to (b)

(a), (b), and (c) are all unequal

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

Correct answer:

(a) is equal to (c)

Explanation:

Calculate the expressions to compare the values: 

a)  of  is 

b)  of  is 

c)  of   is 

(a) and (c) are equal, but (b) is not

Example Question #44 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

(a) is equal to (b).

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

(a) is equal to (c).

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

Correct answer:

(a) is equal to (c).

Explanation:

Simplify each of the expressions to see if they are equal:

a) 

b) 

c) 

Therefore (a) is equal to (c), but not (b).

Example Question #45 : Non Geometric Comparison

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

a)  percent of 

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

Calculate all the expressions to compare the values:

a)  percent of  

b)  

c)  

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

Example Question #46 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

(a), (b), and (c) are all unequal if

(a) is equal to (b) but not (c)

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

(a) is equal to (c) but not (b)

Correct answer:

(a), (b), and (c) are all unequal if

Explanation:

Try substituting a number in for  . Here, we try 

(a) 

(b) 

(c) 

None are equal!

 

If we use , all of the answers will be .

Example Question #81 : Hspt Quantitative Skills

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

a)  of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

Calculate each fraction to compare the values:

a)  of   is .

b)  of  is .

c)  of  is .

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

Example Question #48 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

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

(a) is equal to (b) but not (c).

(a) is equal to (c) but not (b).

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

Correct answer:

(a) is equal to (b) but not (c).

Explanation:

Distribute (a) to compare it to (b) and (c)

a)  

b) 

c) 

Therefore (a) is equal to (b), but not (c).

Example Question #49 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

(b) is equal to (c) but not (a)

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

(a), (b), and (c) are all not equal

(a) is equal to (c) but not (b)

Correct answer:

(a), (b), and (c) are all not equal

Explanation:

Distribute (c) to compare it to (a) and (b):

a) 

b) 

c)  

Simplified, it is evident that all three equations are not equal. You can also try substituting a number in for , and you will get three different values.

Example Question #50 : Non Geometric Comparison

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

a)  of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

Calculate the expressions to compare the values:

a) 

b)

c)

 

Notice that (c) is estimated. The real value is slightly lower. We do not need to go through the exact calculation to compare these values, however. It is clear that (b) is smaller than (a), which is smaller than (c).

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