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Sub 505 Level|   Algebra|               
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Damouse
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piyushpachori
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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miweekend
piyushpachori
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.

Answer: B.

Hope it's clear.
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