Lesson: Introduction to Exponents

Comment on Introduction to Exponents

Hey Brent,

regarding this Q with exponents and inequalities:


In the two statements, since I don´t know the sign I can´t simply divide or multiply. But can I do si if I consider the case of x being positive and x being neg.? It worked out for me on this one.

To be more specific:

Stmt 1: 1/x > -1

case 1 (x pos): -1<x
case 2 (x neg): 1<x

thus, insuff.

Stmt 2: 1/x^5>1/x^3

case 1 (x pos): 1>x
case 2 (x neg.): 1>x

thus, suff.

Is that possible? or did it luckily work out with the specific set of numbers in that particular Q?

gmat-admin's picture

Question link: https://gmatclub.com/forum/gmat-diagnostic-test-question-79337.html

Without seeing your full solution, it's hard to tell whether the steps you took are valid.

That is, for Statement 2 you write:
case 1 (x pos): 1 > x
case 2 (x neg.): 1 > x
These are correct conclusions (for each case), but how did you arrive at those conclusions?


I assumed two cases for the statement: Case 1 x being negative, so when I multiplied by x I switched the < and the other case assuming x being positive, so I miltiplied but didn´t switch the <.

However, I just noticed that when doing that for stmt 2 (which actually yields an answer), I get for assuming x being neg. and pos. respectively two contradicting results. So I guess my approach is invalid?
gmat-admin's picture

Sorry, but I'm still not 100% clear on your solution.
For statement 2, are you multiplying both sides by x or x^3 or x^5?
In the meantime, Bunuel provides a nice solution here: https://gmatclub.com/forum/gmat-diagnostic-test-question-79337-20.html#p...

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