OG-12 PS 130

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Thu Jun 09, 2011 6:40 am

suppose the line is shaded from -5 to +3 (both included).

we are asked to write a equation for this line.

options

a> |x| <=3
b> |x| <=5
c> |x-2| <=3
d> |x-1| <=4
e> |x+1| <=4

OA is E

I know how to solve this. But cant recall the concept as to why the equation is written as a mod.
Just because solving the mod gives us the values x>=-5 and x<=3 ?

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Source: Beat The GMAT — Problem Solving | Thu Jun 09, 2011 6:40 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Thu Jun 09, 2011 7:34 am

-5<=x<=3
-4<=x+1<=4
|x+1|<=4
IMO E

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jun 09, 2011 11:44 am

-5--------------3

Which of the following inequalities is an algebraic
expression for the shaded part of the number line
above [including -5 and 3]?

a> |x| <=3
b> |x| <=5
c> |x-2| <=3
d> |x-1| <=4
e> |x+1| <=4

A very efficient approach would be to use POE (process of elimination).

Since x=-5 is part of the range, x=-5 must satisfy the inequality contained in the correct answer choice.
A quick scan of the answer choices shows that A, C and D can be eliminated:
A) |-5| â‰¤ 3. Doesn't work.
C) |-5-2| â‰¤ 3. Doesn't work.
D) |-5-1| â‰¤ 4. Doesn't work.

Answer choice B can be eliminated because |x| â‰¤ 5 includes x=5, which is not part of the given range.

The correct answer is E.

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