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What is the value of (x - y)^4? (1) The product of x and y is 7. (2) x and y are integers.

Should be C. If x and y are integers and the product of x and y is 7 then we can determine the value of x and y...which is either 1 and 7 or 7 and 1. Both cases generate same value of (x-y)^4, which is 6^4.

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(1) The product of x and y is 7, well this one is clearly insufficient: if \(x=7\) and \(y=1\) then \((x-y)^4=6^4\) and if \(x=14\) and \(y=\frac{1}{2}\) then \((x-y)^4=(\frac{27}{2})^4\), two different answers, hence not sufficient.

(2) x and y are integers. Also insufficient.

(1)+(2) As \(x\) and \(y\) are integers and \(xy=7\) then either \(x\) and \(y\) are 1 and 7 (or vise-versa) or -1 and -7 (or vise-versa) in any case because of even power: \((x-y)^4=(7-1)^4=(1-7)^4=(-7+1)^4=(-1+7)^4=6^4\). Sufficient.

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