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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is 2/3. If there are 36 green marbles in the jar, how many red marbles are there in the jar?

(A) 18
(B) 24
(C) 54
(D) 72
(E) 108

答案和解析

答案：D

解析：

Choice (D) is correct. Let r be the number of red marbles in the jar. The probability of selecting a red marble is equal to the number of red marbles divided by the total number of marbles. Since the probability of selecting a red marble is 2/3, it follows that 2/3 = number of red marbles/total number of marbles. There are 36 green marbles and r red marbles, so the previous equation becomes 2/3 = r/(r + 36). This simplifies to 2(r-36) equals 3r, or (2r)-72 equals 3r. Therefore, the number of red marbles, r, is 72.