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If m and n are positive integers, and m=2n and k=3m, then - 13 May 2021, 03:15
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If m and n are positive integers, and m=2n and k=3m, then -

A) m/2 is a factor of k.
B) 2m is a factor of k.
C) 3m is a factor of k/2.
D) k is a factor of m.
E) k is a factor of m/2.
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A
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Bunuel
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If m and n are positive integers, and m=2n and k=3m, then - 16 May 2021, 07:00
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Bunuel
If m and n are positive integers, and m=2n and k=3m, then -

A) m/2 is a factor of k.
B) 2m is a factor of k.
C) 3m is a factor of k/2.
D) k is a factor of m.
E) k is a factor of m/2.
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m=2n --> m is even.
k=3m --> m is factor of k, thus m/2 = integer must also be a factor of k.

Answer: A.
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If m and n are positive integers, and m=2n and k=3m, then - 13 May 2021, 03:25
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Bunuel
If m and n are positive integers, and m=2n and k=3m, then -

A) m/2 is a factor of k.
B) 2m is a factor of k.
C) 3m is a factor of k/2.
D) k is a factor of m.
E) k is a factor of m/2.
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m=2n and k=3m

i.e. k=3m = 6n

i.e. k is divisible by both m and n as well as by 2 and 3

since m = 2n therefore, m/2 = n

Since, we know that n is a factor of k therefore m/2 will also be a factor of k

Answer: Option A

ALTERNATIVE:

Assume some values of m, n and k as per the given relations

k=3m = 6n
i.e. if n = 1 then m = 2 and k = 6
Now check options

A) m/2 is a factor of k. CORRECT as m/2=1 which is factor of 6
B) 2m is a factor of k. INCORRECT because 2m=4 is NOT factor of 6
C) 3m is a factor of k/2. INCORRECT because 3m=6 is NOT factor of 6/2=3
D) k is a factor of m. INCORRECT because 6 is NOT factor of 2
E) k is a factor of m/2. INCORRECT because 6 is NOT factor of 1
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If m and n are positive integers, and m=2n and k=3m, then - 16 May 2021, 09:38
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If m and n are positive integers, and m=2n and k=3m, then -
k= 3m =6n

A) m/2 is a factor of k. -> Correct, if n= 1, m= 2 and k=6.
B) 2m is a factor of k. -> 2m = 4 is not factor of K= 6. Incorrect.
C) 3m is a factor of k/2. -> 3m= 6 is a factor of K/2 =3. Incorrect.
D) k is a factor of m. -> k=6 is a factor of m =2. Incorrect.
E) k is a factor of m/2. -> k =6 is a factor of m /2 =1. Incorrect.

So, I think A. :)
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If m and n are positive integers, and m=2n and k=3m, then - 16 May 2021, 23:37
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If m and n are positive integers, and m=2n and k=3m, then -

m = 2n ['n' is factor of 'm'] => \(\frac{m}{2} = n\)
K = 3m ['m' is factor of 'k']

k = 3 * 2n = 6n ['n' is factor of 'k']

=> Since, \(n = \frac{m}{2}\) then it is also factor of k.

Answer A
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If m and n are positive integers, and m=2n and k=3m, then - 19 May 2021, 21:59
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Given
    • m and n are positive integers.
    • m=2n and k=3m.

To find
    • The correct option

Approach and Working out:
    • m = 2n and k = 3m
      o k = 3(2n) = 6n


A) m/2 is a factor of k.
    • m/2 = n and n is a factor of k.
    • This option is correct.


B) 2m is a factor of k.
    • 2m = 4n and 4n is not a factor of 6n.
    • This option is not correct.


C) 3m is a factor of k/2.
    • 3m = 6n and 6n is not a factor of 3n(k/2)
    • This option is not correct.


D) k is a factor of m.
    • 6n is a multiple of 2n and not a factor.
    • This option is not correct.


E) k is a factor of m/2.
    • If k is not a factor of m then it will not be a factor of m/2.
    • This option is not correct.


Hence, option A is the correct answer.
Correct Answer: Option A
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If m and n are positive integers, and m=2n and k=3m, then - 02 Jan 2025, 00:19
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