Lesson: QC Strategy - Matching Operations

Plugging in a negative value for a variable is not the same as multiplying both quantities by a negative number.

That approach can get you into trouble. If you use the Plugging In Numbers approach, you can't just stop at plugging in one value, since there might be other values of w such that the two quantities are equal or Quantity B is greater (for more on this, watch the part that starts at 2:50 of this video: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

For example, let's say that we're told that w > 0 and we have the following:
QUANTITY A: w
QUANTITY B: w^2

Using your approach, we might plug in w = 2 (since we're told that w > 0, and 2 > 0). When we do this, we get:
QUANTITY A: 2
QUANTITY B: 4
Here, Quantity B is greater. Does this mean the correct answer is B?
No.

If we plug in w = 1, we get:
QUANTITY A: 1
QUANTITY B: 1
Here, the two quantities are equal.

If we plug in w = 1/2, we get:
QUANTITY A: 1/2
QUANTITY B: 1/4
Here, Quantity A is greater.

So, be careful; plugging in ONE value will not always yield the correct answer.

We are, indeed, "canceling" y - 3x^2 from both quantities. This video is meant to show HOW that works. We do so, by performing the same operation to both quantities.

The term "cancel" can sometimes be misinterpreted. It doesn't mean that, if both quantities share the same algebraic expression, then we can just eliminate those expressions from both quantities.

For example, if we have:
QUANTITY A: 3/x
QUANTITY B: 2/x
We can't just say "Since both expressions have an x term, we just cancel them to get:
QUANTITY A: 3
QUANTITY B: 2
This will yield an incorrect conclusion.

So, we need to be careful to follow the rules/guidelines outlined in the video.

You're referring to the question that appears at 1:37 in the above video:

Given: w > 0
QUANTITY A: 7w + 4
QUANTITY B: w - 2

For Quantitative Comparison questions involving variables, it's often useful to get all of the variables to just one of the quantities. In most cases, that will make it easier to compare the quantities.

Cheers,
Brent

I'm happy to help!

Question link: https://greprepclub.com/forum/m-p-and-x-are-positive-integers-3017.html

Here's my solution: https://greprepclub.com/forum/m-p-and-x-are-positive-integers-3017.html#...

Cheers,
Brent

I address this concept at 2:45 in the above video.

However, I'll show you why dividing both quantities by a negative can lead to false conclusions.

Let's say we're asked to compare the following:
QUANTITY A: -6
QUANTITY B: 12

Clearly Quantity B is greater. In fact, if we follow any of the allowable operations, Quantity B will always be greater.

However, if we break one of the rules and divide both quantities by -3, we get:
QUANTITY A: 2
QUANTITY B: -4
Now, Quantity A is greater.

I hope that helps.

Cheers,
Brent

That's a perfectly valid solution. Nice work!