### All HSPT Quantitative Resources

## 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

**Possible Answers:**

(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)

**Correct answer:**

(a) is four times greater than (c)

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)

**Possible Answers:**

(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)

**Correct answer:**

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

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

**Possible Answers:**

**Correct answer:**

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)

**Possible Answers:**

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

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

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

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

**Correct answer:**

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

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 #55 : 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) is equal to (c) but not (b)

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

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

**Correct answer:**

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

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)

**Possible Answers:**

**Correct answer:**

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 #57 : Non Geometric Comparison

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

a)

b)

c)

**Possible Answers:**

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

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

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

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

**Correct answer:**

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

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)

**Possible Answers:**

**Correct answer:**

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)

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

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

**Possible Answers:**

**Correct answer:**

Multiply each fraction by the proportion described in words:

a) half of

b) double

c) quarter of

With a common denominator, you can compare the fractions and see that (a) is smaller than (c), which is smaller than (b).

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