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by gibran » Thu May 15, 2008 9:03 am
If x < 0 and 0 < y < 1, which of the following has the greatest value?
A. x^2
B. (xy)^2
C. (x/y)^2
D. x^2/y
E. (x^2)(y)

Is there a shorter way to solve this instead of substituting values?
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by AleksandrM » Thu May 15, 2008 9:16 am
I don't really see a shorter way. The shortest way would be to know properties of numbers so well that you do not need to plug them in, you simply think of them in terms of the answer choices. I am certainly not at that level. I still had to plug in. Curious to see what others think.
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by Magellan » Thu May 15, 2008 9:21 am
I would approach is like this:

You have X^2 everywhere, so you can just ignore it and focus on the Y part of the problem.

You should just think that Y has a "good" (i.e. the final answer will be greater) effect when it is in the denominator and a "bad" effect when it is in the numerator.
--> Keep only C and D

Since Y has a good effect in the denominator, it will be better to have it inside the square. (it is better to divide by 1/4 (=multiply by 4) than to divide by 1/2 (=multiply by 2)
--> Choice C

Is that the correct answer?
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by m51v50 » Thu May 15, 2008 9:58 am
Magellan,

Rethink this by inserting saome values:
Say, x=-10 and y = 1/2
Then, (x/y)^2 =100*4=400
And in D: 100*2=200.
So, C is the greatest.
Have 790 or die
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by Magellan » Thu May 15, 2008 10:56 am
I said C as well
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