### All HSPT Quantitative Resources

## Example Questions

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

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

a)

b)

c)

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

(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.

**Correct answer:**

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

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)

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

(a) and (b) are equal

(b) is less than half of (a)

(c) is more than (b)

(b) and (c) are equal

**Correct answer:**

(b) is less than half of (a)

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)

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

(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.

**Correct answer:**

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

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

**Possible Answers:**

(a) is the smallest.

(b) is the smallest.

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

(c) is the smallest.

**Correct answer:**

(c) is the smallest.

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)

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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).

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