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2014/15 AHSMC Part 1 Problem 3

Problem 3 of 16

Let a>b>0a > b > 0 be prime numbers. Of the following five numbers, the one which cannot be equal to a−ba - b is

Answer choices

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Solution

We have 43−2=4143 - 2 = 41, 47−5=4247 - 5 = 42, 47−3=4447 - 3 = 44 and 47−2=4547 - 2 = 45. In order for a−b=43a - b = 43, we must have b=2b = 2 but then a=45a = 45 is not a prime number. The answer is (C).

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