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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 over 3. If there are 36 green marbles in the jar, how many red marbles are there in the jar?

Answer Choices

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Explanation

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 over 3, it follows that 2 over 3 = number of red marbles over total number of marbles. There are 36 green marbles and r red marbles, so the previous equation becomes 2 over 3 = r over (r + 36). This simplifies to 2 times (r plus 36) equals 3 times r, or (2 times r) plus 72 equals 3 times r. Therefore, the number of red marbles, r, is 72.

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