Lesson: Inequalities - Part II

Reinforcement Activities

The topics covered in the above video lesson are commonly tested on the GMAT. So be sure to reinforce you learning by answering several of the practice questions here. Brent, the course creator, has provided detailed solutions to most of the questions.

Comment on Inequalities - Part II

iamstudying - February 8, 2022
Hi Brent, regarding this question:
https://gmatclub.com/forum/if-a-b-c-0-is-c-219680.html

Are we able to use the transitive property here?
S1: Rewritten S1 as 1 < a+b-c. Using given a+b+c < 0 it means that a+b+c < 0 < 1 < a+b-c, thus a+b+c < a+b-c. Subtract a and b on both sides --> c < -c, which means c is a negative number and therefore c<1.

Thank you.
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gmat-admin - February 8, 2022

Question link: https://gmatclub.com/forum/if-a-b-c-0-is-c-219680.html

Great solution! Perfectly reasoned!!
Nice work.

ankitbarnwal7 - October 1, 2023
Question Link:
https://gmatclub.com/forum/is-1-p-r-r-2-2-1-p-r-2-r-86165.html

Where is the problem if we solve like this?

Is 1/p > r/(r^2 + 2)?

The question is asking:
r^2 +2 > pr ??

From stmt 1 we know:
r^2 +2 > r^2 ..so why s the answer not A

Is it the case because we are squaring and missing the negative aspect of r?
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gmat-admin - October 1, 2023

Link: https://gmatclub.com/forum/is-1-p-r-r-2-2-1-p-r-2-r-86165.html

Target question: Is 1/p > r/(r^2 + 2)?

You made an error when rephrasing the target question.

Since r^2 + 2 is always POSITIVE, we can safely multiply both sides of the inequality by (r^2 + 2) to get the rephrased target question: Is (r^2 + 2)/p > r?

IMPORTANT: If we multiply both sides of an inequality by a POSITIVE value, the direction of the inequality symbol STAYS THE SAME. If we multiply both sides of an inequality by a NEGATIVE value, the direction of the inequality symbol IS REVERSED.

So, IF p > 0, we can multiply both sides by p to get: Is r^2 + 2 > pr?
IF p < 0, we can multiply both sides by p to get: Is r^2 + 2 < pr?

Since we don't know whether p is POSITIVE or NEGATIVE, we don't know what the rephrased target question is.

Does that help?

ankitbarnwal7 - October 1, 2023
Makes Sense!
thanks, Brent.

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