Source: Manhattan Prep
If \(x, y\), and \(z\) are positive integers such that \(x < y < z\), is \(x\) a factor of the even integer \(z\)?
1. \(x\) and \(y\) are prime numbers whose sum is a factor of 57.
2. \(y\) is not a factor of \(z\).
The OA is A
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If \(x, y\), and \(z\) are positive integers such that
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The factors of 57 are all odd. If x and y are two different primes, and x+y equals one of those odd factors, one of x or y must be even. But the only even prime is 2, and 2 is the smallest prime, so if x < y, then x = 2 must be true. So x is certainly a factor of the even number z, and Statement 1 is sufficient.
Statement 2 is irrelevant (our numbers could be 2, 3, 4 and the answer could be 'yes', or 4, 5, 6 and the answer could be 'no'), so the answer is A.
Statement 2 is irrelevant (our numbers could be 2, 3, 4 and the answer could be 'yes', or 4, 5, 6 and the answer could be 'no'), so the answer is A.
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