Lesson: QC Strategy - Looking for Equality

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Comment on QC Strategy - Looking for Equality

For the last example where Quantity A had (x-16)(x-7)(x-4) and where Quantity B had (x-9)(x-11)(x-7); why didn't you divide both Quantities by (x-7) since it was present in both cases, and then performed "FOIL" to better cancel out x2 and -20x from both sides leaving you with 64 for Quantity A and 99 for Quantity B?

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.
greenlight-admin's picture

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 so much :)

In the previous video, it said that if you use different "nice" numbers there is a chance that even though in the first few answers both quantities are equal, there is still a chance that they are not, in this video, if you find two conflicting results in the beginning is there no need to keep testing?
greenlight-admin's picture

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 supremely awesome! I'm so totally in love with your videos right now!
greenlight-admin's picture

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

In the last example, I simply eliminated the common binomial (x-7) and then plugged in a value for X which made the calculations faster as I was left with two binomials on each side as opposed to three. Not sure why that wasn't done.
greenlight-admin's picture

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 following way,
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...
greenlight-admin's picture

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?

Best ever explanation
greenlight-admin's picture

Thanks!

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