SAT Math Multiple Choice Practice Question 198: Answer and Explanation

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Question: 198

22. Set S contains the numbers {1, 2, 3, . . . , 15}. If a number is chosen at random from the set, what is the probability that the number is prime?

A. 1/5
B. 4/15
C. 1/3
D. 2/5
E. 7/15

Correct Answer: D

Explanation:

D. Recall that prime numbers are numbers that are only divisible by themselves and 1. Also recall that 1 is not prime (it's "special"), and that 2 is the only even prime. Therefore, the primes that are less than 16 are 2, 3, 5, 7, 11, and 13. Each of the other numbers in the set is divisible by a number besides 1 and itself (15, for example, is divisible by 1, 3, 5, and 15). So you have 6 prime numbers, and there are 15 numbers in the set. Now you see that the probability of picking a prime number is 6/15 = 2/5. Choice (D) is the correct answer.

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