# comparing fractions with variables

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The question is:

We're told that x does not equal zero.

Quantity A: (1+x)/x

Quantity B: (1-x)/x

I thought the answer would be D because I multiplied both sides by x to be comparing 1+x and 1-x, and either one of those can be bigger.

I understand the solution at http://www.greenlighttestprep.com/module/gre-arithmetic/video/1073 but mine should work too.

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Multiplying both sides by x is valid because x is not zero. However, you don't know whether or not x is positive or negative, so if you just eliminate x, you are losing some information! That is why your answer is wrong, but the video is correct.

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Thanks TakeruK!

Shoot. I should know that already.I think I've made that exact same mistake before. More coffee!!!!

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I'd test numbers here. Comparing simple expressions is usually easier by testing numbers than trying to simplify or rewrite the expressions somehow.

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The question is:

We're told that x does not equal zero.

Quantity A: (1+x)/x

Quantity B: (1-x)/x

I thought the answer would be D because I multiplied both sides by x to be comparing 1+x and 1-x, and either one of those can be bigger.

I understand the solution at http://www.greenlighttestprep.com/module/gre-arithmetic/video/1073 but mine should work too.

Hi dux3000,

This QC can be solved by TESTing VALUES and defining the pattern that exists.

IF...X = 1, then...

A = (1+1)/1 = 2

B = (1-1)/1 = 0

Quantity A is bigger

IF...X = -1, then...

A = (1+ -1)/-1 = 0

B = (1- -1)/-1 = -2

Quantity A is bigger

IF...X = -2, then...

A = (1+ -2)/-2 = +1/2

B = (1- -2)/-2 = -3/2

Quantity A is bigger

This pattern will continue on no matter what VALUES you TEST for X; Quantity A is ALWAYS Bigger, so the answer is A.

GRE Masters aren't born, they're made,

Rich

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Hi Rich,

How do you know quantity A is ALWAYS bigger?

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