SAT Math: Exponents | Quiz One: Practice

1. John is older than Maria. Maria is younger than Sue. Terry is the oldest of the four of them. Who is the youngest?

John

Maria

Sue

Terry

They are all the same age

J > M
M T > (J,M, and S)
So,
M Maria is the youngest.

Explanation

J > M
M T > (J,M, and S)
So,
M Maria is the youngest.

2. Solve for x: 2x + 3 = 4x - 3

0

1

3

5

7

2x + 3 = 4x - 3
3 = 2x - 3
6 = 2x
3 = x

Explanation

2x + 3 = 4x - 3
3 = 2x - 3
6 = 2x
3 = x

3. A set of integers includes: 44, 66, 88, and x. If the mean of the scores is 80, what is x?

12

104

120

122

200

(44 + 66 + 88 + x)/4 = 80
44 + 66 + 88 + x = 320
x = 320-88-66-44
x = 122

Explanation

(44 + 66 + 88 + x)/4 = 80
44 + 66 + 88 + x = 320
x = 320-88-66-44
x = 122

4. In a class election between Ricky, Susie, and Mikey, Ricky earns 20% of the vote and Mikey earns 30% of the vote. There are 24 members of the class. How many votes did Susie receive?

4

8

12

16

20

First, you will need to know Susie's percentage: 100% - 30% - 20% = 50%

Second, you should multiply that percentage by the total number of votes: 50% * 24 = .5 * 24 = 12

Explanation

First, you will need to know Susie's percentage: 100% - 30% - 20% = 50%

Second, you should multiply that percentage by the total number of votes: 50% * 24 = .5 * 24 = 12

5. If Pete can run five miles in one hour, how many hours would it take him to run 25 miles?

3

4

5

10

15

5 miles / 1 hr = 5 mph
25 miles / 5 mph / 5 miles.

Explanation

5 miles / 1 hr = 5 mph
25 miles / 5 mph / 5 miles.

6. (5 * 5 + 3) / 2 + 7 / 7 = ?

1

7

14

15

35

5 * 5 = 25 + 3 = 28
28/2 = 14
14 + 1 = 15

Explanation

5 * 5 = 25 + 3 = 28
28/2 = 14
14 + 1 = 15

7. A fair coin is flipped three times. What is the chance that no head will appear?

1/8

1/4

1/3

1/2

0

The chance of no heads appearing is the same as the chance of all tails appearing, which is: (1/2)^3 or 1/8

Explanation

The chance of no heads appearing is the same as the chance of all tails appearing, which is: (1/2)^3 or 1/8

8. The letters of the word: "alphabets" are placed into a hat and scrambled. What is the probability of choosing a vowel at random from the hat?

1/12

1/6

1/3

2/9

4/9

The vowels are: a,e,i,o, and u. "alphabet" has 2 a's and 1 e, or 3 vowels total out of 9 letters. 3/9 = 1/3.

Explanation

The vowels are: a,e,i,o, and u. "alphabet" has 2 a's and 1 e, or 3 vowels total out of 9 letters. 3/9 = 1/3.

9. A six-sided dice is rolled twice. What is the chance that the sum of the two rolls will be exactly 10?

1/12

1/16

3/7

1/6

3/8

10 = 5 + 5, 4 + 6, 6 + 4

The probability of any given combination is (1/6)^2 = 1/36

There are three combinations

3*1/36 = 3/36 = 1/12.

Explanation

10 = 5 + 5, 4 + 6, 6 + 4

The probability of any given combination is (1/6)^2 = 1/36

There are three combinations

3*1/36 = 3/36 = 1/12.

10. A number is given as 3513N, where N is an positive integer that fills in the units digit. Which of the following values of N would result in 3513N being a multiple of 9?

3

4

5

6

7

For a number to be a multiple of 9, the sum of its digits must be a multiple of 9. Since 3 + 5 + 1 + 3 = 12, N must be 6.

Explanation

For a number to be a multiple of 9, the sum of its digits must be a multiple of 9. Since 3 + 5 + 1 + 3 = 12, N must be 6.

11. If the length of the sides of a cube is tripled, by what factor is the volume of the cube increased?

3

6

9

15

27

V = s^3
so V of the new cube = (3s)^3 = 3^3*s^3 = 27s^3

27s^3/s^3 = 27

Explanation

V = s^3
so V of the new cube = (3s)^3 = 3^3*s^3 = 27s^3

27s^3/s^3 = 27

12. If Mike can buy four apples for one pear and four pears for one peach, and if one peach is equal to eight bananas, how many bananas will Mike receive for two apples?

1

2

4

6

8

4 apples = 1 pear 4 pears = 1 peach 1 peach = 8 bananas So, 1 apple = 1/4 pear 1/4 pear = 1/8 peach 1/8 peach = 1 banana. So, 1 apple = 1 banana

Explanation

4 apples = 1 pear 4 pears = 1 peach 1 peach = 8 bananas So, 1 apple = 1/4 pear 1/4 pear = 1/8 peach 1/8 peach = 1 banana. So, 1 apple = 1 banana

13. If a block has dimensions of 3, 4, and 5 units, how many 2 by 2 by 3 blocks can fit in the block?

4

5

8

12

15

V(big block) = 3*4*5 = 60
V(small block) = 2*2*3 = 12

V(big)/V(small) = 4 small blocks.

Explanation

V(big block) = 3*4*5 = 60
V(small block) = 2*2*3 = 12

V(big)/V(small) = 4 small blocks.