### All HSPT Quantitative Resources

## Example Questions

### Example Question #61 : 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) equals (c) but not (b)

To compare the expressions, distribute and simplify:

a)

b)

c)

It is now clear that (a) and (c) are equal but (b) is not.

### Example Question #61 : How To Make Non Geometric Comparisons

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 unequal

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

**Correct answer:**

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

The important property of square roots to remember here is that

This means that (a) can be broken up into the following:

These variations are all equal

### Example Question #63 : Non Geometric Comparison

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

a)

b)

c)

**Possible Answers:**

**Correct answer:**

(a) is exactly half of (b) , and is therefore smaller. (c) is even smaller than both.

### Example Question #64 : 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), (b), and (c) are all equal

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

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

**Correct answer:**

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

One way to test this answer is to substitute in numbers for the variables. For example, let's say that and :

a)

b)

c)

None are equal!

### Example Question #65 : Non Geometric Comparison

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

a) of

b) of

c) of

**Possible Answers:**

**Correct answer:**

Multiply the fractions by the integers in order to compare the expressions:

a)

b)

c)

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

### Example Question #66 : 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) equals (c) and is less than (b)

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

(a) equals (c) and is greater than (b)

**Correct answer:**

(a) equals (c) and is greater than (b)

The property of exponents to remember here is that .

This means that .

.

### Example Question #67 : Non Geometric Comparison

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

(a)

(b)

(c) percent

**Possible Answers:**

**Correct answer:**

Converted into decimals, the numbers look like this:

a)

b)

c) percent

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

### Example Question #68 : 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), (b), and (c) are all equal

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

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

**Correct answer:**

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

Try substituting a number in for to test this problem. Here, we try .

a)

b)

c)

It is now evident that (a) and (b) are equal, but not (c)

### Example Question #61 : How To Make Non Geometric Comparisons

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 unequal

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

**Correct answer:**

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

(b) is a factored version of (a). (c), however, is not raised to the same exponent. Test this by plugging a number in for . Here, we try .

a)

b)

c)

(a) and (b) are equal, but (c) is not.

### Example Question #70 : Non Geometric Comparison

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

a) percent

b)

c)

**Possible Answers:**

**Correct answer:**

Convert each to a decimal in order to compare them:

a)

b)

c)

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

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