# HSPT Quantitative : Non-Geometric Comparison

## Example Questions

### Example Question #41 : Non Geometric Comparison

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

a)

b)

c)

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 #41 : Non Geometric Comparison

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

a)  percent of

b)  of

c)  of

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

(a) is equal to (c)

(a) is equal to (b)

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

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

(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)

(a) is equal to (b).

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

(a) is equal to (c).

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

(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 #42 : Non Geometric Comparison

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

a)  percent of

b)

c)

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 #41 : How To Make Non Geometric Comparisons

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

a)

b)

c)

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

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

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

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

(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

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)

(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.

(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)

(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)

(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

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).