GRE Quant Ep 7: Inequalities & Absolute Values

Inequalities and Absolute Values might cause more problems than any other in the GRE Quant section. The intricate algebra you need for some questions makes this a really challenging topic.

In this video, Harry -- a GMAT Ninja tutor -- will help you understand inequalities and absolute values, and how the GRE will structure questions on these topics. He'll help you understand the content and how to apply the necessary processes to answer a GRE quant question involving inequalities or absolute values (or both!) accurately and efficiently.

This is video #7 in our series of full-length GRE quant lessons. For updates on upcoming videos, please subscribe!

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Chapters:
00:00 Introduction
02:02 Question 1 - Basic Inequalities
07:30 Question 2 - Basic Absolute Values
13:28 Question 3 - Dividing by a Variable
17:21 Question 4 - Positive or Negative?
21:20 Question 5 - Multiple Inequalities
28:55 Question 6 - Inequalities AND Absolute Values
34:51 Question 7 - Substitutions Involving Inequalities
40:30 Question 8 - Using Logic
47:13 Question 9 - The Same or Different?
53:34 Question 10 - Gratuitously Difficult Problem

[GokhanSenerPhD]

I just solved the last question in 40 seconds, and now I am 100% sure I will get into a respected business PhD program. Also, you have some serious sick gainz bro!

[hamzaa.]

Thanks for the tips.
For the questions such as the one in 34:50, I think it is more time efficient to do the algebra manipulation..

[_saanchishah]

For the question at 46:41- Taking approximately 0 won't be accurate right? If P is any integer greater than 0 (which it is) - Quantity B will always be greater because pq will always be negative (since q < -2). The only reason you picked D is because you approximated P to 0 which doesn't hold true. Please explain...?

[Journey-to-Clarity-]

For question 7, does the question says those are integers?, without the information we cannot pick anything right? Said in HOW to approach video, can u pls clarify this. 38:10

[yessbenne]

To simlify absolute values, see the two cases x > 0 aand x<0

[HarshPatel-bvrz]

Great explanation. For Question 6, wouldn't t have to be greater than 1 to satisfy the given in the problem statement? "t" must be greater than t/|t|

[kofiadaba]

I don't know how valid this is, but for question 10, my approach was at x maximum, x is approximately equal to y therefore quantity A becomes the absolute value of y-a which is less than the absolute value of x-b therefore quantity B is greater

[ynigam]

For question 7, answer choice A would assume that p is positive, right? Because if p was negative, then B would be greater?

[tosynademilua]

For question 3, can we take bc to the other side so we have ac-bc <0. Then factor out c to have c(a-b)<0

So c <0 ; a-b<0

a < b ?

[jesuslover]

Please I would like to ask if 3m= -5n, then 3m+5n < 0 since both 3m and 5n are negative numbers. can you please explain how you got 3m+5n=0

Thank you!
your videos are really helpful

[rabbathussain]

We can write quantity A, |3m + 5n|, as |3m + 3m -24| and quantity B, |3m| + |5n|, as |3m| +|3m|
This simplifies to quantity A being |6m - 24| and quantity B as |6m|. If m < 0 then quantity A is greater than B. If m > 0 then B is greater. Hence should the answer not be D, cannot be determined?

[antony]

Question 7; assuming p takes a value of -1, We could prove that Quantity B>Quantity A, so shouldn't the answer be D?

[ugonnaumeh]

love your work guys, but for question 7 how about if p was a negative won't B be larger. therefor D is our final answer

[AdedoyinAdekunle-zk]

Thank you so much for this video. I totally understand the explanation you gave in question 8, but I am still not clear on why for question 7, you didn't apply the same rule of close estimation as you did to question 8. For question 7, both solutions gave different answers, why isn't it possible to choose option D since it wasn't stated that x, y were integers?

[kritinbhardwaj]

Hello, whats stopping us considering the value of y to be less than 0 in the 7th question and approaching a value such that the value of x-y/5 becomes negative
Ex: x=15p and y=-16p

[Abkuyper]

50:01 isn't it, + - 3m = + - 5n? why you only said 3m = + - 5n?

[shanedepoe]

on question 6, why do you have two different answers? wouldn't t=-1 so that it doesn't violate the original t/I t I is less than t ? why do you flip the sign at all?

[oluwatobiaderemi]

If T = 0.5, T is still greater than 0, But T over T is not less than T right?

[PrinceSharma-gy]

In question 9 why you didn't do 3m= 24+5n and put it in quantity A then |24 + 10n | that is 24 more than to quantity B if substitute|3m| to |5n| then quantity B will be | 10n| hence Quantity A is 24 more than quantity B

[martynadydyk]

How come the last one was the easiest one lol