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13 Apr 2019, 13:48
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:29) correct
45%
(02:09)
wrong
based on 208
sessions
History
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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.
(1) P is completely divisible by 5.
(2) Q is completely divisible by 5.
13 Apr 2019, 23:06
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Manang
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
Answer: Option D
General Discussion
07 Jul 2019, 12:15
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3P – Q – 5 = 0
From S1:
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.
From S2:
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 = 5/3. Not possible as P and Q are positive integers.
Min value of Q has to be 5.
Same case as S1.
HCF (P,Q) = 5.
SUFFICIENT.
D is the answer.
From S1:
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.
From S2:
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 = 5/3. Not possible as P and Q are positive integers.
Min value of Q has to be 5.
Same case as S1.
HCF (P,Q) = 5.
SUFFICIENT.
D is the answer.
