Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

X / |X| < x
<=> X / |X| - x < 0
<=> x*(1-|x|) < 0 as |x| > 0 and this inequation is not using x = 0 as a possibility, which is prohibited
<=> x*(|x| - 1) > 0
<=> sign(x) = sign(|x|-1)

In other word, we have to know
o for which x > 0, |x|-1 > 0
o for which x < 0, |x|-1 < 0

o If x > 0, then
|x|-1 > 0
<=> x - 1 > 0
<=> x > 1

o If x < 0, then
|x|-1 < 0
<=> -x - 1 < 0
<=> x > -1.... So 0 > x > -1

That means :
0 > x > -1 OR x > 1.... In other word x must be superior to -1.

Re: Absolute Expressions [#permalink]
01 Nov 2007, 14:24

Fig wrote:

gluon wrote:

bmwhype2 wrote:

X / |X| <x> 1 x > -1 |X| <1> 1

A is correct.

(A) x > 1
Assume x = 2 then we get 2 / |2| = 1 which is LESS than 2. Hence, correct.
This would be true for any value of x > 1

(B) x > -1
Assume x = 0.5 then we get 0.5 / |0.5| = 1 which is MORE than 0.5. Hence, wrong.
So all the values of x > -1 do not satisfy X / |X| <x>-1 satisfies all the values.

B is not saying everything greater than (-1) WORKS. It just states every value of x that DOES work must be > (-1). In order to kill B you must find something smaller than (-1) that works, and that seems impossible.

(-.5) seems to kill choice A, no? It's smaller than 1 and it gives us (-1) < (-.5). No problem there. So I'm going with B.

Ok, plugging any value > -1 makes it correct, it's B.

Fig or beckee529, help me understand this. Correct me what I am doing wrong below:

For +ve X,

X/X < X yields 1 <X> 1

For -ve X,

-X/-X < -X yields 1 < -X or we can say X < -1 When I say X < -1, it means X can be -2, -3, -4.........etc.

These absolute questions are tricky.

It's in your way to replace |x|/x < x when x is negative.... U have to replace only |x| by -x. The rest remains unchanged as they do not have to be positive all time

Ok, plugging any value > -1 makes it correct, it's B.

Fig or beckee529, help me understand this. Correct me what I am doing wrong below:

For +ve X,

X/X < X yields 1 <X> 1

For -ve X,

-X/-X < -X yields 1 < -X or we can say X < -1 When I say X < -1, it means X can be -2, -3, -4.........etc.

These absolute questions are tricky.

It's in your way to replace |x|/x < x when x is negative.... U have to replace only |x| by -x. The rest remains unchanged as they do not have to be positive all time

Fig, thanks for pointing out the wrong step. It makes sense now.

It’s been a long time, since I posted. A busy schedule at office and the GMAT preparation, fully tied up with all my free hours. Anyways, now I’m back...

Burritos. Great, engaging session about how to network properly. How better can it get? Hosted jointly by Human Capital Club and Engineers in Management, we had a chance to...