SAT Math Multiple Choice Practice Question 174: Answer and Explanation

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Question: 174

20. a and b are both positive integers greater than one. If a is a factor of both b + 2 and b - 3, then b could equal

A. 21
B. 25
C. 29
D. 33
E. 37

Correct Answer: D

Explanation:

D. b + 2 and b - 3 differ by 5, so any number that goes into both of them must also go into 5. But the only numbers that go into 5 are 1 and 5, and you know that a is bigger than 1, so a = 5. On the list of answer choices, 33 is the only possibility for b because 33 + 2 = 35 and 33 - 3 = 30, and both of these numbers are divisible by 5.

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