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.

6. What is the 7th number in the series?

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.