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If \(x\) is a positive integer, is \(x\) a prime integer?

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Source: — Data Sufficiency |

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by Ian Stewart » Tue May 07, 2019 5:26 am

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Statement 1 tells us x is one less than some prime number. If that prime is 3, then x=2, and x is prime, but if that prime is 5, x=4, and x is not prime, so Statement 1 is not sufficient.

Statement 2 tells us x is 5 greater than some prime number. If that prime is 2, then x=7, and x is prime, but if that prime is any other prime, then that prime will be odd and x will be even (and will not be 2), so x will not be prime. So Statement 2 is not sufficient.

But notice that if both Statements are true, x cannot be 7, because then Statement 1 is false, so if both Statements are true, x is 5 greater than some odd prime, and x is even (and is not 2), so is not prime, and both statements are sufficient together. The answer is C.
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