SAT Practice Math Questions

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. 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.

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. 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

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 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.

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 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

10. 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.

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 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

To determine how many 2 by 2 by 3 blocks can fit inside a larger block with dimensions of 3 by 4 by 5 units, you need to calculate the volume of each block and then divide the volume of the larger block by the volume of the smaller block.

The volume of the larger block: Volume = Length x Width x Height = 3 x 4 x 5 = 60 cubic units

The volume of a single 2 by 2 by 3 block: Volume = Length x Width x Height = 2 x 2 x 3 = 12 cubic units

Now, divide the volume of the larger block by the volume of the smaller block to find out how many of the smaller blocks can fit: Number of smaller blocks = Volume of larger block / Volume of smaller block Number of smaller blocks = 60 cubic units / 12 cubic units = 5

Explanation

To determine how many 2 by 2 by 3 blocks can fit inside a larger block with dimensions of 3 by 4 by 5 units, you need to calculate the volume of each block and then divide the volume of the larger block by the volume of the smaller block.

The volume of the larger block: Volume = Length x Width x Height = 3 x 4 x 5 = 60 cubic units

The volume of a single 2 by 2 by 3 block: Volume = Length x Width x Height = 2 x 2 x 3 = 12 cubic units

Now, divide the volume of the larger block by the volume of the smaller block to find out how many of the smaller blocks can fit: Number of smaller blocks = Volume of larger block / Volume of smaller block Number of smaller blocks = 60 cubic units / 12 cubic units = 5

13. 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

1. Find the value of apples in terms of pears:

Mike can buy 4 apples for 1 pear, so 1 apple is equal to 1/4 pear.

2. Find the value of pears in terms of peaches:

Mike can buy 4 pears for 1 peach, so 1 pear is equal to 1/4 peach.

3. Find the value of apples in terms of peaches:

Since 1 apple = 1/4 pear and 1 pear = 1/4 peach, then 1 apple = (1/4) * (1/4) = 1/16 peach.

4. Find the value of peaches in terms of bananas:

1 peach = 8 bananas

5. Find the value of apples in terms of bananas:

Since 1 apple = 1/16 peach and 1 peach = 8 bananas, then 1 apple = (1/16) * 8 = 1/2 banana.

6. Find the value of two apples in terms of bananas:

2 apples = 2 * (1/2 banana) = 1 banana

Therefore, Mike will receive 1 banana for two apples.

Explanation

1. Find the value of apples in terms of pears:

Mike can buy 4 apples for 1 pear, so 1 apple is equal to 1/4 pear.

2. Find the value of pears in terms of peaches:

Mike can buy 4 pears for 1 peach, so 1 pear is equal to 1/4 peach.

3. Find the value of apples in terms of peaches:

Since 1 apple = 1/4 pear and 1 pear = 1/4 peach, then 1 apple = (1/4) * (1/4) = 1/16 peach.

4. Find the value of peaches in terms of bananas:

1 peach = 8 bananas

5. Find the value of apples in terms of bananas:

Since 1 apple = 1/16 peach and 1 peach = 8 bananas, then 1 apple = (1/16) * 8 = 1/2 banana.

6. Find the value of two apples in terms of bananas:

2 apples = 2 * (1/2 banana) = 1 banana

Therefore, Mike will receive 1 banana for two apples.