# HSPT Quantitative : Non-Geometric Comparison

## 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

(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)

(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)

(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)

(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

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)

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

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

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

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

(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 #52 : Non Geometric Comparison

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

a)

b)

c)

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

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

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

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

(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)

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 #52 : How To Make Non Geometric Comparisons

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

a)

b)

c)

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

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

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

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

(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)

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)

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

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

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

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

(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