Lesson: Inequalities - Part II

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Just want to make sure I'm understanding right... how do you know for sure that x+5 at the end will result in y < x < x +5 < w?

Also on a separate note, it seems that the lessons in the prior chapters kind of build on each other and vice versa and whatnot... (i.e. this video will help me with # property questions and arithmetic questions). Was there a certain reason behind why you ordered your quant video chapters the way they are? Thanks!
gmat-admin's picture

We're told that y < x AND x + 5 < z

So, once we recognize that it is always the case x < x + 5, then we can combine the two inequalities.

I spent A LOT of time thinking about the order in which the topics appear. My goal was to make sure that, if learning concept C requires knowledge about concept A, then concept A must appear before concept C.

For example, we need to know how to collect like terms (i.e., 7x - 2x = 5x) before we can solve basic equations (like 7x - 9 = 2x + 11). So, the video on collecting like terms appears before basic equation solving.

And so on...

thank you - I love your course thus far and am def spreading the word!
gmat-admin's picture

Thanks! I appreciate that.

Hi Brent,

For the final example in the video, can we write the relationship between y and w as follows,

y < x < w-5

gmat-admin's picture

You're referring to the question that begins at 4:55 in the video.

Yes, your inequality is good. You just need to keep going, because we're asked to compare y and w (not y and w-5)

Given: y < x
x + 5 < w

You took the second inequality and subtracted 5 from both sides to get: x < w - 5

Then you combined this with the first inequality to get: y < x < w-5

Since we're trying to compare y and w, we need to recognize that w-5 < w for all values of w

So, we can add this last part to your inequality to get:
y < x < w-5 < w, which means we can be certain that y < w

Hi Brent,

I was looking for some lessons in inequalities with powers and roots. Do you have a video lesson that covers concepts involving these. For eg. x^2 < 81 means -9 < x < 9. What happens if you take the square root on both sides of the original inequality? I'm finding this concept difficult to grasp. Any help is appreciated. Thanks.
gmat-admin's picture

You're referring to quadratic inequalities, and they're typically pretty tricky questions. Here's the video that covers that concept:


Great. Thanks!

Hi Brent,
I am not able to find answer for this question on beatthegmat. http://www.beatthegmat.com/x-and-y-t276919.html
I know earlier there was your answer on this topic but its not visible now.Can you please give me link of this question's answer.
If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y
gmat-admin's picture

Hi Neha,

I have posted my solution here: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-is-x-y-x-5-y...


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