IAS Mathematics, Questions and ans

1) If both x and y are prime numbers, which of the following CANNOT be the difference of x and y?
(A) 1
(B) 3
(C) 9
(D) 15
(E) 23

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Answer: Choice E is correct. This problem is solved fastest by process of elimination. Both 2 and 3 are prime and their difference is one (Eliminate Choice A). Both 5 and 2 are prime and their difference is 3 (Eliminate Choice B). Both 11 and 2 are prime and their difference is 9 (Eliminate C). Both 17 and 2 are prime and their difference is 15 (Eliminate D)