HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #61 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

(a) equals (b) but not (c)

(a) equals (c) but not (b)

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

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

Correct answer:

(a) equals (c) but not (b)

Explanation:

To compare the expressions, distribute and simplify:

a)  

b)  

c) 

It is now clear that (a) and (c) are equal but (b) is not.

Example Question #61 : How To Make Non Geometric Comparisons

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

a) 

b) 

c) 

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

The important property of square roots to remember here is that 

This means that (a) can be broken up into the following:

These variations are all equal

Example Question #63 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

(a)  is exactly half of (b) , and is therefore smaller. (c)  is even smaller than both.

Example Question #64 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

One way to test this answer is to substitute in numbers for the variables. For example, let's say that  and :

a) 

b) 

c) 

None are equal!

Example Question #65 : Non Geometric Comparison

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

a)  of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

Multiply the fractions by the integers in order to compare the expressions:

a) 

b) 

c) 

It is now clear that (b) is smaller than (a), which is smaller than (c).

Example Question #66 : 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

(a) equals (c) and is less than (b)

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

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

Correct answer:

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

Explanation:

The property of exponents to remember here is that .

This means that .

.

 

Example Question #67 : Non Geometric Comparison

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

(a) 

(b) 

(c)  percent

Possible Answers:

Correct answer:

Explanation:

Converted into decimals, the numbers look like this:

a) 

b) 

c)  percent 

It is now evident that (c) is smaller than (a), which is smaller than (b)

 

Example Question #68 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

(a) equals (b) but not (c)

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

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

(a) equals (c) but not (b)

Correct answer:

(a) equals (b) but not (c)

Explanation:

Try substituting a number in for  to test this problem. Here, we try .

a) 

b) 

c) 

It is now evident that (a) and (b) are equal, but not (c)

Example Question #61 : How To Make Non Geometric Comparisons

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

a) 

b) 

c) 

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

(b) is a factored version of (a). (c), however, is not raised to the same exponent. Test this by plugging a number in for . Here, we try .

a) 

b) 

c) 

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

Example Question #70 : Non Geometric Comparison

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

a)  percent

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

Convert each to a decimal in order to compare them:

a) 

b) 

c) 

It is now evident that (a) is smaller than (c), which is smaller than (b).

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