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# Does 2m - 3n = 0 (1) m ≠ 0 (2) 6m = 9n

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Q33  V19
Re: Does 2m - 3n = 0 (1) m ≠ 0 (2) 6m = 9n [#permalink]
piyushpachori wrote:
The question is not asking you to find possible values of (m,n). You are not required to do this at all. All you need to find out is whether 2m -3n = 0

Rewrite the question prompt as -
=> 2m = 3n
=> m/n = 3/2

Statement 1 - m != 0; This tells us nothing about 'n'. Insufficient.
Statement 2 - 6m = 9n => m/n = 3/2 ; The ratio m/n is same as that in the question prompt. Sufficient.

Ans. B

I probably complicate myself but still wish to clarify if this can be E.

Since the question didn't indicate it is m & n are both INTEGER, so put fraction into considerations as well.
When I put in
m = 2, n = 3 or m = 1/2, n = 1/3, B comes valid...so isn't it a vague question? or I missed any important step? pls advise..thanks
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Re: Does 2m - 3n = 0 (1) m ≠ 0 (2) 6m = 9n [#permalink]
miweekend wrote:
piyushpachori wrote:
The question is not asking you to find possible values of (m,n). You are not required to do this at all. All you need to find out is whether 2m -3n = 0

Rewrite the question prompt as -
=> 2m = 3n
=> m/n = 3/2

Statement 1 - m != 0; This tells us nothing about 'n'. Insufficient.
Statement 2 - 6m = 9n => m/n = 3/2 ; The ratio m/n is same as that in the question prompt. Sufficient.

Ans. B

I probably complicate myself but still wish to clarify if this can be E.

Since the question didn't indicate it is m & n are both INTEGER, so put fraction into considerations as well.
When I put in
m = 2, n = 3 or m = 1/2, n = 1/3, B comes valid...so isn't it a vague question? or I missed any important step? pls advise..thanks

You are right we are not told that m and n are integers, though we can get that statement (2) is sufficeint even not knowing that.

Does 2m - 3n = 0

Question basically asks whether $$2m=3n$$

(1) $$m\neq{0}$$ --> clearly insufficient as no info about n.
(2) $$6m=9n$$ --> reduce by 3: $$2m=3n$$, so this statement directly answers the question (so here it doesn't matter whether m and n are integers). Sufficient.

Hope it's clear.
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Re: Does 2m - 3n = 0 (1) m 0 (2) 6m = 9n [#permalink]
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Re: Does 2m - 3n = 0 (1) m 0 (2) 6m = 9n [#permalink]
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