SAT Math Multiple Choice Practice Question 244: Answer and Explanation

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Question: 244

2. Two positive integers are "compatible" if their greatest common factor is a prime number. For instance, 15 and 25 are compatible because their greatest common factor is 5, which is prime. If m and 98 are compatible, and m is an odd number, then what is the greatest common factor of m and 98?

A. 2
B. 5
C. 7
D. 14
E. 49

Correct Answer: C

Explanation:

C Since the prime factorization of 98 is , and since the greatest common factor of m and 98 is a prime number, that greatest common factor must be 2 or 7. Since it is not even, it must be 7.

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