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
What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive integers?
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Let's take each statement one by one.BTGmoderatorDC wrote: ↑Sun Feb 16, 2020 5:17 pmWhat 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
1) P is completely divisible by 5.
Say P = 5x.
From 3P – Q – 5 = 0, we have 3*5x – Q – 5 = 0 => 15x – Q – 5 = 0
=> Q = 5(3x – 1)
Case 1: Say x is even, then 3x – 1 = odd; thus, HCF of P = 5x and Q = 5(3x – 1) is 5 since x and (3x – 1) are co-prime.
Case 2: Say x is odd, then 3x – 1 = even; thus, HCF of P = 5x and Q = 5(3x – 1) is 5 since x and (3x – 1) are co-prime.
Sufficient.
2) Q is completely divisible by 5.
With the same reasoning as done in Statement 1, we get HCF = 5. Sufficient.
The correct answer: D
Hope this helps!
-Jay
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