HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #51 : Non Geometric Comparison

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

a)  percent of 

b)  percent of 

c)  percent of 

Possible Answers:

(a) is two times greater than (b)

(a) is two times greater than (c)

(a) is four times greater than (b)

(a) is four times greater than (c)

Correct answer:

(a) is four times greater than (c)

Explanation:

Calculate each expression to compare the values:

a)  percent of  is:

b)  percent of  is:

 

c)  percent of  is:

 

(a) and (b) are equal, and (a) is four times greater than (c) because:

Example Question #51 : 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), (b), and (c) are all equal

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

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

Correct answer:

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

Explanation:

In (b), the expressions are multiplied. Both the coefficents and variables are multiplied together:

In (b), the terms are added together. Since they are like terms, the coefficients simply add together:

Now that everything is simplified, we can tell that they are all unequal.

Example Question #53 : 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 each expression to compare the values:

a)  of 

b)  of 

c)  of 

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

Example Question #51 : 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) is equal to (c) but not (b)

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

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

Correct answer:

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

Explanation:

When two elements are multiplied inside of a square root, it is the same as if each of their square roots were multiplied together. Therefore (a) simplifies like this:

This is equal to (b), but not (c)

Example Question #55 : 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) is equal to (c) but not (b)

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

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

Correct answer:

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

Explanation:

Simplify each expression to compare them. Remember for (c) that an exponent outside of parentheses distributes to each of the elements inside:

a) 

b)  

c)  

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

Example Question #56 : Non Geometric Comparison

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

a) 

b)  percent

c) 

Possible Answers:

Correct answer:

Explanation:

Convert each value to a decimal to compare them:

a)  

b)  percent 

c)  

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

Example Question #57 : 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), (b), and (c) are all unequal

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

Correct answer:

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

Explanation:

When doing these calculation, be sure to follow the order of operations and do the multiplication before the addition:

a) 

b) 

c) 

(a) and (c) are both , but (b) is 

Example Question #58 : Non Geometric Comparison

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

a) 

b) 

c) 

Possible Answers:

Correct answer:

Explanation:

Choose a common denominator to compare the fractions. One choice is , because its factors include , and :

a) 

b) 

c) 

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

Example Question #52 : 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), (b), and (c) are all equal

Explanation:

Both  and  convert to the same decimal: 

Since each of these portions are multiplied by , all expressions are equal.

Example Question #60 : Non Geometric Comparison

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

a) half of 

b) double 

c) quarter of 

Possible Answers:

Correct answer:

Explanation:

Multiply each fraction by the proportion described in words:

a) half of 

b) double 

c) quarter of 

With a common denominator, you can compare the fractions and see that (a) is smaller than (c), which is smaller than (b).

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