Lesson: Simplifying Expressions

Comment on Simplifying Expressions

Can we divide both sides by x+y
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-79...

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?


Oh yh that's true. Thanks

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://gre.myprepclub.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...



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

Question link: https://gre.myprepclub.com/forum/is-a-negative-integer-and-is-a-nonnegat...

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://gre.myprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-795.html
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/gre-math-challenge-137-x-y-and-2-x-y-79...

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.

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.

Hey Brent i have a simple question 4/4 =1 or zero can u explain this to me please and thank u
greenlight-admin's picture

In general, if k ≠ 0, then k/k = 1
So, 4/4 = 1

You can also think of 4/4 as 4 ÷ 4.
How many times does 4 divide into 4? 1 time. So, 4/4 = 1

Hey Brent

2^x + 2^x = 2^1(2^x) but not 2^2x as terms not multiplying and not 4^x as we are not adding constant only...... so whenever like terms come i should combine them by taking a common out and using product rule later? but if they are multiplying i use product rule direct?

greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/2-x-2-x-688.html

In the same way that k + k = 2k, we can say that 2^x + 2^x = 2(2^x)
Since 2(2^x) = (2^1)(2^x), we must apply the Product Law since we are finding the product of 2 powers with the same base.

The other laws don't apply here, since we are finding the product of 2 powers with the same base.

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