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04 Jun 2023, 03:59
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Statement 1.
6 * 11
6 * 13
Both have 6 as hcf. Infinite such numbers are possible.
A and D out
Statement 2
The factors of 36 that are greater than 6 are 9, 12, 18, and 36.
M and N pairs as (9,12 ), (9, 36), (12, 18), and (12, 36)
Multiple possibilities
B out
Statements 1 and 2
(9,12 - GCD 3), (9, 36 - GCD 9), (12, 18 - GCD 6), (12, 36 - GCD 12)
Of all possibilities, only 12,18 satisfies having GCD as 6
Hence C is the correct answer
Also, note that hcf * lcm = M * N
hcf = 6
lcm = 36
M * N = 216
Again only 12,18 satisfies
6 * 11
6 * 13
Both have 6 as hcf. Infinite such numbers are possible.
A and D out
Statement 2
The factors of 36 that are greater than 6 are 9, 12, 18, and 36.
M and N pairs as (9,12 ), (9, 36), (12, 18), and (12, 36)
Multiple possibilities
B out
Statements 1 and 2
(9,12 - GCD 3), (9, 36 - GCD 9), (12, 18 - GCD 6), (12, 36 - GCD 12)
Of all possibilities, only 12,18 satisfies having GCD as 6
Hence C is the correct answer
Also, note that hcf * lcm = M * N
hcf = 6
lcm = 36
M * N = 216
Again only 12,18 satisfies
26 Aug 2024, 18:08
Kudos
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(1) The greatest common divisor of M and N is 6
M and N can be wriiten as 6a and 6b , where a and b are coprime(no common factors except 1).
Hence, NOT sufficient.
(2) The least common multiple of M and N is 36
It is clear from this that Value of max of M and N is < or = 36.
also, the only prime factors in M and N are 2,3. We cannot determine N.
(M,N) can be (12, 36) or (12, 18)
After combing St1 & 2,
We know that there no common factor between M and N except 6.
Also, N>M. Only case possible is (M,N) = (12, 18)
N = 18
Sufficient.
Answer C.
M and N can be wriiten as 6a and 6b , where a and b are coprime(no common factors except 1).
Hence, NOT sufficient.
(2) The least common multiple of M and N is 36
It is clear from this that Value of max of M and N is < or = 36.
also, the only prime factors in M and N are 2,3. We cannot determine N.
(M,N) can be (12, 36) or (12, 18)
After combing St1 & 2,
We know that there no common factor between M and N except 6.
Also, N>M. Only case possible is (M,N) = (12, 18)
N = 18
Sufficient.
Answer C.
AbdurRakib
08 Sep 2025, 13:33
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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