# HSPT Quantitative : How to make non-geometric comparisons

## Example Questions

### Example Question #31 : How To Make Non Geometric Comparisons

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

a)

b)

c)

Explanation:

Each of these expressions can made to look like the other two through factoring or distributing:

(a) becomes (b) by distributing the .

(c) becomes (b) by distributing the .

(b) becomes (a) by factoring out , (c) by factoring out .

### Example Question #32 : How To Make Non Geometric Comparisons

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

a)  of

b)  percent of

c)

(b) is greater than (a) or (b).

(a) is equal to (c).

(c) is greater than (a) or (b).

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

(c) is greater than (a) or (b).

Explanation:

Calculate the expressions to compare the values:

a)  of

b)  percent of

c)

Now it is clear that (a) and (b) are equal, and (c) is greater than both of them.

### Example Question #33 : How To Make Non Geometric Comparisons

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

a)

b)

c)

Explanation:

Calculate the expressions to compare the values:

a)

b)

c)

Now, it is clear that (c) is greater than (b), which is greater than (a).

### Example Question #34 : How To Make Non Geometric Comparisons

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

a)

b)

c)

(a) and (b) are equal

(b) is less than half of (a)

(c) is  more than (b)

(b) and (c) are equal

(b) is less than half of (a)

Explanation:

When solving this problem, make sure to follow the order of operations: first parentheses, then exponents, and finally addition.

a)

b)

c)

None are equal, and (c) is much more than  more than (b). Those answers are therefore false. (b) is less than half of (a) because  is less than half of .

### Example Question #31 : Non Geometric Comparison

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

a)  percent of

b)

c)

Explanation:

To easily compare them, turn each expression into a decimal:

a)  percent of

b)

c)

Now it is clear that (a) is greater than (b), which is greater than (c)

### Example Question #36 : How To Make Non Geometric Comparisons

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

a)

b)

c)

Explanation:

Follow the order of operations when solving these problems: first parentheses, then exponents, then multiplication, then addition.

a)

b)

c)

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

### Example Question #37 : How To Make Non Geometric Comparisons

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

a)

b)

c)

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

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

(b) is greater than (a) or (c).

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

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

Explanation:

The only operations in these expressions are addition and subtraction. According to the order of operations, these are on the same level. That means we can reorder the numbers as much as we want, throw parentheses in wherever, and still get the same answer. Just make sure to keep track of what numbers are positive or negative. In this problem, (a), (b), and (c) all equal .

### Example Question #38 : How To Make Non Geometric Comparisons

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

a)  of

b)  of

c)  of

(a) is the smallest.

(b) is the smallest.

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

(c) is the smallest.

(c) is the smallest.

Explanation:

Calculate each expression to compare the values.

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

a)  of

b)  of

c)  of

Therefore (c) is the smallest, and (a) and (b) are equal.

### Example Question #31 : How To Make Non Geometric Comparisons

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

a)

b)

c)

Explanation:

Calculate each expression to compare them:

a)

b)

c)

Therefore (a) and (b) are equal, and (c) is larger than both of them.

### Example Question #40 : How To Make Non Geometric Comparisons

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

a)

b)

c)  percent

Explanation:

Convert everything to a decimal to be able to compare them more easily:

a)

b)

c)  percent

Now it is clear that (a) and (b) are equal, and they are both greater than (c).