##### 1. What is the difference between 3.8 and 0.571?

- 0.73
- 2.567
- 3.229
- 4.262

##### 2. 2.567 rounded to the nearest hundredth is:

- 2.6
- 3.0
- 2.56
- 2.57

##### 3. Dividing a number by 2 is the same as multiplying that number by

- 2
- 1
- 1/4
- 1/2

##### 4. Arrange the following numbers in order from the least to greatest 2^{3}, 4^{2}, 6^{0}, 9, 10^{1}.

- 2
^{3}, 4^{2}, 6^{0}, 9, 10^{1} - 6
^{0}, 9, 10^{1}, 2^{3}, 4^{2} - 10
^{1}, 2^{3}, 6^{0}, 9, 4^{2} - 6
^{0}, 2^{3}, 9, 10^{1}, 4^{2} - 9, 6
^{0}, 10^{1}, 4^{2}, 2^{3}

##### 5. If *a* = -6 and *b* = 7, then 4a (3b+5) + 2b = ?

- 638
- 624
- 610
- -610
- -638

##### 6. If one person consumes 8 glasses of water on a daily basis, how many glasses of water will 18 people consume?

- 26
- 64
- 128
- 144

##### 7. A woman weighs 145 pounds. She gains 12 pounds one month and 6 pounds the next month. What is her new weight?

- 151 pounds
- 153 pounds
- 157 pounds
- 163 pounds

##### 8.Expand the following expression:

(2x – 20) (5x + 10)

- 10x
^{2 }– 80x – 200 - 70x – 200
- 10x
^{2 }– 80x + 200 - 10x
^{2 }– 120x – 200

##### 9. For what real number x is it true that 3(2x – 10) = x ?

- -6
- -5
- 5
- 6
- 30

##### 10. Henry is three times as old as Truman. Two years ago, Henry was five times as old as Truman. How old is Henry now?

- 4
- 8
- 12
- 16
- 20

##### Answers and Explanations

###### 1. C

The word “difference” signifies a subtraction problem. When subtracting decimals, align the decimals vertically. The result is 3.229, Choice C.

###### 2. D

Look at the digit in the thousandths place. In this case it is a 7. Since the number is 5 or greater, round up the digit in the hundredths place. The correct answer is 2.57, Choice D.

###### 3. D

Division is the opposite, or the reciprocal, of multiplication. If you divide a number by 2, you have to multiply it by 1/2 to get the same result.

**4. D**

When a number is raised to a power, it is multiplied by itself as many times as the power indicates. For example,2^{3}=2*2*2=8. A number raised to the power of 0 is always equal to 1, so 6^{0} is the smallest number shown. Similarly, for the other numbers:9=9;10^{1}=10;4^{2}=4*4=16.

**5. E**

Substitute the given values for the variables into the expression:

4a (3b+5) + 2b = 4 * -6 (3 * 7 + 5) + 2 * 7

Using order of operations, compute the expression in the parentheses first.

Remember that you must first multiply 3 by 7and then add 5 in order to follow order of operations:

= 4 * -6(21 + 5) + 2 * 7 Next, add the values in the parentheses.

= 4 * -6(26) + 2 * 7 Simplify by multiplying the numbers outside the parenthesis.

= -24(26) + 14 Multiply -24 by 26.

= -624 +14 Add.

= -610

**6. D**

To find the total amount that will be consumed, multiply the number of glasses consumed by one person (8) by the number of people indicated in the question (18): 8 x 18 = 144.

**7. D**

To calculate her new weight, add her weight increases (12 pounds and 6 pounds) to her original weight (145 pounds): 145 pounds + 12 pounds + 6 pounds = 163 pounds.

**8. A**

Use the FOIL method (first, outside, inside, and last) to get rid of the parentheses:

(2x – 20) (5x + 10) = 2x(5x) + 2x(10) – 20(5x) – 20(10) = 10x^{2 }+ 20x – 100x – 200.

Then, combine like terms to simplify the expression:

10x^{2 }– 80x – 200.

**9. D**

To solve 3(2x – 10) = x, first multiply out the left side of the equation using distribution: 6x – 30 = x. After subtracting x from both sides, we have 5x – 30 = 0. Finally, adding 30 to both sides results in 5x = 30, and therefore x = 6.

**10. C**

To solve this problem, first let *h *represent Henry’s age and let *t *represent Truman’s age. Since Henry is three times as old as Truman, then *h *= 3*t*. Note that two years ago, Henry’s and Truman’s ages would be *h *– 2 and *t *– 2, respectively.Then, since Henry was five times as old as Truman two years ago, we have *h *– 2 = 5(*t *– 2).

By substituting *3t *for *h*, we can solve the following equation: 3*t *– 2 = 5(*t *– 2).

3*t *– 2 = 5*t *– 10

8 = 2*t*

*t = *4

So, Truman is 4 years old and Henry is three times Truman’s age, or age 12, Choice C.