Quant Comparison Question

[safirshahbaaz90]

Hi Tommy,

Please help with the following quant comparison question:

Quantity A: ((6a)^0.5) * (5(3)^0.5)
Quantity B: (200a)^0.5

I think the answer is D, because "a" can be positive or negative. But, the book from where I picked this question has considered only the positive value of "a" and thus says that quantity A is greater.

Please help! Do I have to ignore the negative value of "a"? In a previous post, we had discussed that only positive value of number should be chosen but for variables, we should consider both positive and negative. It would be really sad to lost out on a point because of this :(

Regards,
Safir

[tommywallach]

Hey Safir,

What source is this question from? It should've specified that a had to be greater than 0. Otherwise the answer is D because a can be zero. (Don't worry about negative square roots, which are never tested on the GRE.)

-t

Work:

Quantity A = rt. 6 * rt. a * rt. 125 = rt. 750a
Quantity B = rt. 200a

If a is 0, the two quantities are equal. If a is anything positive, Quantity A is bigger.

[safirshahbaaz90]

Hi Tommy,

Thanks for the answer. Just to be really sure, when you say I can ignore -ve roots of x, then rt(x) will always be positive? But we had a discussion sometime back that for variables we need to consider both +ve and -ve values. I'm really confused. Please help.

Regards,
Safir

[tommywallach]

Hey Safir,

No no. I didn't say that. In your original post, you wrote "I think a can be positive or negative." I'm saying it can't, because they will never ask you to take the square root of a negative number. The RESULT could be negative, but the input (the thing IN the radical) will not be negative.

-t

[safirshahbaaz90]

Oh OK.. Thanks :)

[tommywallach]

No problem!

-t