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# SAT Math Practice 1: Answers and Explanations

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Practice to prepare for SAT Math. Learn the answers and the explanations for these SAT Math sample questions.

Questions Found Here">

(A)  0

(B)  1.7

(C)  4

(D)  3

(E)  0.7

### Explanation

Solve for x:

1. 3x + 2 = 10
2. 3x + 2 + -2 = 10 + -2
3. 3x = 8
4. 3x/3 = 8/3
5. x = 8/3

Find x -1:

8/3 -1 = 5/3 = 1.666666667

### 2. For all real values of p, 0 < p < 1.

Which of the following must be greater than 1?

(A)  p2

(B)  p3

(C)  2p

(D)  p + 5

(E)  10p2

### Explanation

Choose a real number between 0 and 1.
Let p= .2

Test the value, p = .2 in each of the choices.

(A)  p2 = (.2)2 = .04

(B)  p3= (.2)3 = .008

(C)  2p = 2(.2) = .4

(D)  p + 5 = .2 + 5 = 5.2

(E)  10p2 = = 10(.2)2 = .4

### 3. Alfred has a bag of marbles.

There are 12 blue marbles, 18 yellow marbles, 24 red marbles, and the rest of the marbles are green. If the probability of choosing a green marble is 10, then how many green marbles are there?

(A)  10

(B)  6

(C)  60

(D)  42

(E)  5

### Explanation

1.  Add the number of blue, yellow, and red marbles
12 + 18 + 24 = 54

2.  How many green marbles?
Unknown, so g = the number of green marbles

3.  What portion of the total marbles are either blue, yellow, or red?
90 percent
, or .90, because 10 percent, or .10 of the marbles are green

4.  Create a proportion:

54/.90 = g/.10

5. Solve for g:

54 * .10 = .90 * g

5.4 = .90g

5.4/.90 = .90g/.90

6 = g

### 4. The digits of two positive distinct integers are added.

One integer is a multiple of 9. The other integer is a multiple of 3. The sum of the digits cannot be:

(A)  12

(B)  6

(C)  15

(D)  21

(E)  33

### Explanation

Consider a few multiples of 9 and find the sum of the digits:

9:  9

18: 1 + 8 = 9

27:  2 + 7 = 9

108:  1 + 0 + 8 = 9

558:  5 + 5 + 8 = 18

Notice that each sum is at least 9. 6 is the only answer choice that is less than 9.

### 5. .5384615384...

What is the 15th digit behind the decimal?

(A)  5

(B)  3

(C)  8

(D)  6

(E)  4

### Explanation

The pattern for .5384615384 is a repetition of the first 6 digits behind the decimal: 538461. Thus, the 15th digit must be 8.

2, 4, 6, 10, 16…

(A) 24

(B) 26

(C) 14

(D) 42

(E) 50

### Explanation

Remember, that the pattern must be consistent. The only consistent pattern is this:

• 2 + 4 = 6  (2, 4, 6, 10, 16)
• 4 + 6 = 10 (2, 4, 6, 10, 16)
• 6 + 10 = 16 (2, 4, 6, 10, 16)

Therefore, the 7th number in the series must be the sum of 16 and 26: 42.

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