motion2020 wrote:
\(x\), \(y\) and \(z\) are positive integers such that \(1 < x < y < z\). If the product of \(x\), \(y\) and \(z\) is 399, what is \(z-y\) ?
Source: Manhattan Review, GMAT Question Bank
Given: xyz = 399
This suggests that we should find the prime factorization of 399.
When we do this we get: 399 = (3)(7)(19)
Since x < y < z, we can conclude that x = 3, y = 7 and z = 19
So, z - y = 19 - 7 = 12
Answer: 12
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