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# What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive

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What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive  [#permalink]

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13 Apr 2019, 13:48
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Difficulty:

45% (medium)

Question Stats:

63% (01:44) correct 38% (01:59) wrong based on 8 sessions

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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.
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Re: What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive  [#permalink]

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13 Apr 2019, 23:06
1
Manang 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.

Question: HCF of P and Q = ?

Given: 3P – Q – 5 = 0
i.e. 3P – Q = 5

Statement 1: P is completely divisible by 5

Case 1: P = 5, then Q = 10 HCF = 5
Case 2: P = 10, then Q = 25 HCF = 5
Case 3: P = 15, then Q = 40 HCF = 5
Case 4: P = 20, then Q = 55 HCF = 5

i.e. HCF in each case is 5 i.e.

SUFFICIENT

Statement 2: Q is completely divisible by 5

Case 1: P = 5, then Q = 10 HCF = 5
Case 2: P = 10, then Q = 25 HCF = 5
Case 3: P = 15, then Q = 40 HCF = 5
Case 4: P = 20, then Q = 55 HCF = 5

i.e. HCF in each case is 5 i.e.

SUFFICIENT

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Re: What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive   [#permalink] 13 Apr 2019, 23:06
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