Confusing Absolute Value Q

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briology: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun Sep 18, 2011 1:14 am

by briology » Sun Nov 20, 2011 10:23 pm

Hi All--

I find this absolute problem confusing--it seems nonsensical to me. Can someone help?

if Y>=0, what is the value of X?

1. |x-3|>=Y
2. |x-3|<=-Y

Thanks!

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Source: Beat The GMAT — Data Sufficiency | Sun Nov 20, 2011 10:23 pm

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Nov 20, 2011 10:43 pm

Any function inside a modulus is always +ve.
We are given y is 0 or +ve.

Statement 1:

|x-3| is ALWAYS +ve. We're given 'y' is +ve as well. X and Y can have infinite values - Insufficient.

Statement 2:

Again we know |x-3| is +ve. Since 'y' is +ve or 0. LHS will be -ve or 0. (the '-Y' term)

'-Y' CANNOT be -ve as the RHS is always +ve, so it HAS to be 0.

|X-3| = 0 -> X = 3 (Sufficient) B IMO

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Nov 21, 2011 2:35 am

If y>=0, what is the value of X?

1. |x-3|>=Y

Implies x-3 >y or x-3 <-y, Insufficient(too many values)

2. |x-3|<=-Y

The value of |x-3| is > 0
The value of -y is <0. (as y > 0, i.e. -y < 0)
So |x-3| cannot be < y but can only be equal to y at y = 0
x-3 = 0; x =3
Sufficient !

IMO B

Anil Gandham
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