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What is the value of y?

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Source: — Data Sufficiency |

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by Ian Stewart » Sat May 18, 2019 9:58 am

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Each statement is clearly insufficient alone. Using both, from Statement 1 we can factor since we have a difference of squares:

(x + y)(x - y) = 5

From Statement 2, x+y and x-y are both integers, and if x and y are each positive integers, x+y is greater than 1. Since x+y is also clearly a factor of the prime number 5 from the equation above, x+y must equal 5 (since that's the only factor of 5 greater than one), and x-y must therefore equal 1, so we have two simple linear equations we can solve (x = 3 and y =2). The answer is C.
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