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## Comment on

QC Strategy - Looking for Equality## For the last example where

I understand this video is about looking for Equality, but in regards to Equality; (in pausing the video before watching the explanation), I saw what both sides had equally in common (which was (x-7) being multiplied by both sides).

Why then wasn't B the right answer if we used your Matching Operations Strategy verses plugging in possible answers for x (especially when in the Matching Operations' Video the last example where QA was 2x and QB was 3x, that the answer wasn't B because we couldn't be sure of what X was; just like how we're unsure of what x could be in this particular example); wouldn't it be better to try to cancel out all the variables if possible (using the Matching Operations Strategy) to derive to the correct answer?

Thank you in advance; I am truly appreciative.

## You need to be very careful

You need to be very careful when dividing both quantities by a variable or an expression involving variables. First off, you might be dividing both quantities by zero, which can be problematic.

To illustrate what I mean, consider what would happen if Quantity A was (0)(3) and Quantity B was (0)(2). Clearly, the two quantities are equal. However, if we divide both sides by 0, we "seemingly" get Quantity A: 3 and Quantity B: 2.

That's the risk you run by dividing both quantities by (x-7) since it's possible that you could be dividing both quantities by 0.

Also, if you watch the matching operations video (https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...), you'll see that we cannot divide both quantities by a negative value. How can we be certain that (x-7) is not a negative value.

For these reasons, we can't simply divide both quantities by (x-7)

I hope that helps.

## Yes it helps alot, thank you

## In the previous video, it

## Yes, that's the downside of

Yes, that's the downside of testing numbers. If you plug in different numbers but keep getting the SAME result (e.g., on the first test you find that quantity A and quantity B are equal, and on the second test you find that quantity A and quantity B are equal), it's still possible that the two quantities are not always equal. So, you CAN'T be absolutely certain the answer is C.

However, if you plug in two different sets of values and get CONFLICTING results (e.g., on the first test you find that quantity A and quantity B are equal, and on the second test you find that quantity A is greater than quantity B), then you can be CERTAIN that the answer is D.

## These strategies are so

## That's great to hear. Thanks

That's great to hear. Thanks for taking the time to say that!

## In the last example, I simply

## Great question!

Great question!

The strategy you describe will get you in trouble. To understand why, let's examine what you mean by "eliminate." Presumably, you eliminated (x-7) by dividing each side by (x-7). The problem with this strategy is that we don't know the value of x. So, (x-7) can be positive, negative, or zero, and each of these cases alters the outcome when we divide by (x-7).

For example, what if the two quantities were as follows:

Quantity A: 3(x-7)

Quantity B: 2(x-7)

If we divide both quantities by (x-7), we get:

Quantity A: 3

Quantity B: 2

So, is the correct answer B?

No, the correct answer is D. If we plug x = 1 into 3(x-7) and 2(x-7), we see that Quantity A is greater. If we plug plug x = 8 into 3(x-7) and 2(x-7), we see that Quantity B is greater. If we plug in x = 7, the quantities are equal.

For more on acceptable operations you can perform on each quantity, see https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

## Last example we can solve by

a=(x-16)(x-7)(x-4),b=(x-9)(x-11)(x-7)

a=(x-16)(x-4),b=(x-9)(x-11)

a=x2-20x+64,b=x2-20x+99

a=x2+64,b=x2+99

Then B must be greater,So by this process how the answer will be D,Please Sir...

## There's a problem with your

There's a problem with your second step where you eliminated the (x-7) from both quantities. Presumably, you divided both quantities by (x-7)

Since we don't know the value of x, it's possible that you have inadvertently divided both quantities by zero, which will negatively impact your solution.

Also, since we don't know the value of x, it may be the case that (x - 7) is negative, and we have a rule about dividing both quantities by a negative value (for more on this, see: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

Consider this example:

QUANTITY A: 3x

QUANTITY B: 2x

If x = 0, then the two quantities are EQUAL

If x = 1, then quantity A is greater

If x = -1, then quantity B is greater

So, the correct answer here is D.

Now, let's see what happens if we break our rule and divide both sides by x.

We get:

QUANTITY A: 3

QUANTITY B: 2

This would SUGGEST that the correct answer is A, but this is not the case.

Does that help?

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