SAT Math Multiple Choice Practice Question 585: Answer and Explanation

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Question: 585

21.

In a certain game, a red marble and a blue marble are dropped into a box with five equally-sized sections, as shown above. If each marble lands in a different section of the box, how many different arrangements of the two marbles are possible?

A. 5
B. 20
C. 25
D. 40
E. 100

Correct Answer: B

Explanation:

B This is a pattern question, so write it out: If the red marble lands in section 1, the possible red-blue pairs are 1 and 2, 1 and 3, 1 and 4, and 1 and 5. That's 4 possibilities. If the red marble lands in section 2, the possible red-blue pairs are 2 and 1, 2 and 3, 2 and 4, and 2 and 5. We count all four pairs, because though it seems like 1 and 2 is the same as 2 and 1, in both cases we dropped the red marble first, and red and blue is a different arrangement than blue and red. If the red marble lands in 3, the possibilities are 3 and 1, 3 and 2, 3 and 4, and 3 and 5: another 4 possibilities. A red marble in section 4 will give 4 possibilities, and in section 5 will also give 4 possibilities. 4 + 4 + 4 + 4 + 4 = 20, answer B.

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