BTGmoderatorDC wrote:What is the HCF of P and Q if 3P - Q - 5 = 0 and P and Q are positive integers?
1) P is completely divisible by 5.
2) Q is completely divisible by 5.
OA D
Source: e-GMAT
\(3P - Q - 5 = 0\)
From Statement 1:
\(P\) is completely divisible by 5 or \(P\) is a multiple of 5.
\(P\) can be 0, 5, 10, 15, 20, 25...
If \(P = 0\), then \(Q = -5\). Not possible as \(P\) and \(Q\) are positive integers.
Min value of \(P\) has to be 5.
\(P = 5\), then \(Q = 10\)
\(P = 10\), then \(Q = 25\)
\(P = 15\), then \(Q = 40\)
and so on
\(HCF (P,Q) = 5\). Sufficient. \(\Large{\color{green}\checkmark}\)
From Statement 2:
\(Q\) is completely divisible by 5 or \(Q\) is a multiple of 5.
\(Q\) can be 0, 5, 10, 15, 20, 25...
If \(Q = 0\), then \(P = \frac{5}{3}\). Not possible as \(P\) and \(Q\) are positive integers.
Min value of \(Q\) has to be 5.
Same case as Statement 1.
\(HCF (P,Q) = 5\). Sufficient. \(\Large{\color{green}\checkmark}\)
Therefore,
D is the correct answer.
