Question: k's on Both Sides

Comment on k's on Both Sides

This is definitely a quicker way to get the answer but I am still not clear on how it was done. My method was to replace the variable (k) with numbers greater than 0. First I tested both sides by replacing the variable K with 1. In that case, Quantity B was greater than quantity A. Next I tested by replacing variable K with the number 2. In that case Quantity A was greater so I ended up with the same answer D. If I understood the method in the video I would definitely practice it.
greenlight-admin's picture

Your method is great (however, when you replaced k with 1, you should have found that the two quantities are equal). In fact, the strategy you used is covered in this video:

The strategy I used is called Matching Operations. It's covered here:

my way was to plug some positive numbers, then when I saw that the results are not equal and vary between co,umn A and B I decided that the result is D
greenlight-admin's picture

That works too! Just keep in mind that plugging in numbers only yields a conclusive result when the answer is D. For more see (starting at 2:50)

So in a question like this the strategy will be ADD, SUBTRACT AND DIVIDE? if am following you right!!
greenlight-admin's picture

Those are the steps I took for this question, but I would advise against memorizing steps. Just follow the basic guidelines/rules that we cover in this related video:

Notice that I could have taken a different route (while still adhering to the rules of Matching Operations (as covered in the above video). For example...

QUANTITY A: 3k + 5
QUANTITY B: 11 - 3k

Subtract 5 from both quantities to get:
QUANTITY B: 6 - 3k

Add 3k to both quantities to get:

Divide both quantities by 6 to get:

Answer: D

Hello! I dont understand the rules in application here. Are these expressions or equations? Are they related? How can you just add and multiply etc? I hope my question makes sense! Basically, how do you know you're not just making up math rules when doing these types of problems? Thank you for this site also! So helpful.
greenlight-admin's picture

Hi Dsho,

Here, the two quantities are expressions.
So, Quantity A and Quantity B can have a variety of values, depending on the value of k.

Regarding the technique used to answer the question, this video covers everything you need to know:

Please let me know if that helps.


I have a question.
I approach this question by squaring both sides, so I could exclude K and get only positive integers. Why was my solution wrong?
greenlight-admin's picture

That strategy can get you into trouble, because squaring a NEGATIVE will turn that number into a POSITIVE number.

Consider this example:
We can clearly see that Quantity A is bigger

However, if we SQUARE both quantities, we get:
Now Quantity B is bigger

Also, keep in mind that we're already told that k is positive (k > 0)


First check for equal case -

Assume they are equal => 3k+5 = 11-3k

Simplify, get k=1 so when K is 1 both quantities are equal.
At this point we know that we met the equal case,
Now, check for inequality case => plug k=2 in both the quantities.

3(2)+5 11-3(2)

11 11-6 ----> here clearly A is greater.

As such we have 2 answers. The right answer is D

greenlight-admin's picture

Perfectly valid approach - nice work!

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!