Lesson: Simplifying Expressions

Comment on Simplifying Expressions

https://greprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-795.html
Can we divide both sides by x+y
greenlight-admin's picture

Question link: https://greprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-795.html

That would be nice!
However, when it comes to using the Matching Operation strategy, one of the big rules says:
Do NOT multiply or divide both quantities by a NEGATIVE value.
(more at https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...)

Since x+y can be either positive or negative, we can't divide both sides by x+y.

Does that help?

Cheers,
Brent

Oh yh that's true. Thanks

https://greprepclub.com/forum/x-23363.html
I'm getting the answer as A. Here is my approach:
Divide both sides by 'x' which gives us 5 & 2. Hence, A. Why is this approach wrong?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/x-23363.html
The problem with your solution is that you divide both sides by a negative value (since we're told x < -8)
For more on this see: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

Thanks!

https://greprepclub.com/forum/is-a-negative-integer-and-is-a-nonnegative-integer-18960.html

Is 0 classified as a negative or non-negative integor?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/is-a-negative-integer-and-is-a-nonnegative...

0 is neither positive nor negative.
We can refer to 0 as non-negative.
We can also refer to 0 as non-positive.

How about dividing both sides by (x+y)? Then we can arrive at 1<2, hence Answer B https://greprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-795.html
greenlight-admin's picture

Question link: https://greprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-795.html

When answering Quantitative Comparison questions, we must be super careful when dividing both quantities by a variable, since we may be inadvertently dividing by zero or a negative number.

Given:
Quantity A: 1(x+y) [I added the 1 for dramatic effect]
Quantity B: 2(x+y)

If x = 1 and y = -1, then x+y = 0, which means we get:
Quantity A: 1(0)
Quantity B: 2(0)

So, when you divide both quantities by x+y, you're actually dividing by zero.
This means your solution is telling us that 1(0) divided by 0 = 1, and 2(0) divided by 0 = 2, which is not the case.

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