exponents

[cypherskull]

If mn ≠ 0, what is the value of 3m/n^2?

1. 3m^2 = 27n^4
2. n = 4

Can't we simplify (1) to get m = 3n^2?

[neelgandham]

If mn ≠ 0, what is the value of 3*(m/n^2)?

1. 3m^2 = 27n^4

3m^2 = 27*(n^4)
m^2 = 9*(n^4)
m^2/(n^4)=9
(m/(n^2))^2 = 9
So, the value of m/(n^2) can be 3 or -3. and the value of 3*(m/n^2) is 9 or -9.
Since we have two answers to the question, statement 1 is insufficient to answer the question.

2. n = 4

Arrrrggghh!

Can't we simplify (1) to get m = 3n^2?

No, you shouldn't. The value of m = +3n^2

Answer - E

[Anurag@Gurome]

If mn ≠ 0, what is the value of 3m/n^2?

1. 3m^2 = 27n^4
2. n = 4

Statement 1: 3*(m^2) = 27*(n^4) ---> m^2 = 9*(n^4) --> [m/(n^2)]^2 = 9 ---> m/(n^2) = ±3 ---> 3m/(n^2) = ±9

Not sufficient

Statement 2: We don't know the value of m.

Not sufficient

1 & 2 Together: n = 4 ---> m^2 = 9*(4^4) ---> Two possible values of m ---> Two possible values of 3m/(n^2)

Not sufficient

The correct answer is E.

[cypherskull]

Thanks Anil and Anurag. I do have a question though (and excuse me if u find it silly but this part really confuses me). Somewhere in this forum I read that on the GMAT, we should consider sq. root of a positive number to be a positive value only. Got no second thoughts now that I'm wrong, but am I missing something here? In which scenario does that rule apply?

[Anurag@Gurome]

Somewhere in this forum I read that on the GMAT, we should consider sq. root of a positive number to be a positive value only. Got no second thoughts now that I'm wrong, but am I missing something here? In which scenario does that rule apply?

Read my post here >> https://www.beatthegmat.com/gmat-prep-ds ... tml#481767

[Ian Stewart]

Thanks Anil and Anurag. I do have a question though (and excuse me if u find it silly but this part really confuses me). Somewhere in this forum I read that on the GMAT, we should consider sq. root of a positive number to be a positive value only. Got no second thoughts now that I'm wrong, but am I missing something here? In which scenario does that rule apply?

If k is a positive number, then √k means by definition "the positive square root of k". So √k can never be negative, because of the way the square root symbol is defined.

So if you see the expression √16, that cannot be negative, and so certainly must be equal to 4 and nothing else. But there are still two different numbers whose square is 16: 4 and -4. So if there's no square root symbol in your expression to rule out the negative solution, the negative solution will very often be perfectly legitimate. An equation like x^2 = 16 has two perfectly good solutions for x, for example. Or if you know a^2 = b^2, you cannot be sure that a = b; it might be that a = -b.