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rasuti
Students
 
Posts: 1
Joined: Wed Feb 06, 2013 11:01 am
 

Question name: Absolutely less

by rasuti Tue Mar 05, 2013 5:45 pm

x/|x| < x
x does not equal 0



Quantity A Quantity B
|x| 1


I don't understand why the answer isn't A. If x=1, then the inequality above doesn't hold true, so the answer can't be C. I also don't see how absolute value of x can be negative making it less than 1. Help!
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Question name: Absolutely less

by tommywallach Tue Mar 05, 2013 8:59 pm

Hey Rasuti,

Absolute value questions generally revolve around positives and negatives. In this case, after you've tried something logical, such as x = 2, you need to try something crazy. In this case, you need a negative fraction.

x = -(1/2)

Let's make sure it makes the equation true:

x/|x| < x

(-1/2)/|-1/2| < -1/2

(-1/2)/(1/2) < -1/2

-1 < -1/2

That is true, so -(1/2) is a legitimate value for x. It's less than 1, so column A is now smaller that column B. Because x = 2 makes column A bigger than column B, the answer is (D).