Question: Fractions with x and y

Comment on Fractions with x and y

A quick way I arrived at the answer:
First realised that x and y are negative,but that x is greater in magnitude than y (i.e. x is more negative than y). When you divide 1 by a negative number you get a negative fraction; the more negative the denominator the smaller in magnitude the result is (and therefore the less negative it is).
So we are taking a less negative number away from a more negative number, which leaves us with something still on the negative side of the number line.
This explanation is lengthy, but if you realise that about the question, it's a quick way to solve it I think.
greenlight-admin's picture

I love it! That's a great (and perfectly valid) solution that uses some number sense.

May i know why is it that i get a wrong answer when i multiply both columns by 2 in order to get "Y-X" in column A?
greenlight-admin's picture

Given:
QUANTITY A: 1/2y - 1/2x
QUANTITY B: 0

Be careful, if we multiply Quantity A by 2, we don't get y - x.

If we multiply both quantities by 2, we get:
QUANTITY A: 2/2y - 2/2x
QUANTITY B: 0

Simplify to get:
QUANTITY A: 1/y - 1/x
QUANTITY B: 0

That said, let's keep going.
The given information tells us that x and y are both negative.
This means the product xy is POSITIVE

So, let's multiply both quantities by xy to get:
QUANTITY A: xy/y - xy/x
QUANTITY B: 0

Simplify to get:
QUANTITY A: x - y
QUANTITY B: 0

At this point, we can add y to both quantities to get:
QUANTITY A: x
QUANTITY B: y

Since we're told that x < y < -1, we can see that Quantity B is greater.

Does that help?

Cheers,
Brent

if we solve x-y/2xy; here 2xy is positive and x-y is also positive. when both numerator and denominator are positive, it is greater than 0. so A is greater than B-- can you please correct me
greenlight-admin's picture

Almost!
Since x < y, we know that x-y is NEGATIVE (not positive)
So, Quantity A is negative

Pick x = -3, y = -2 and solve part A. Answer is B. BOOM
greenlight-admin's picture

Be careful. Getting B as the correct answer was only coincidental.
Testing ONE set of possible values will not yield a definitive answer here.
When you plug in x = -3 and y = -2 and see that Quantity B > Quantity A, this just tells you that the correct answer is either B or D. That's all you can be certain of. It just happens to be the case that Quantity B is always greater.

I cover this at 2:50 in the following video: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

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