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OG-12 PS 130

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OG-12 PS 130

by bblast » Thu Jun 09, 2011 6:40 am
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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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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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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| ≤ 3. Doesn't work.
C) |-5-2| ≤ 3. Doesn't work.
D) |-5-1| ≤ 4. Doesn't work.

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

The correct answer is E.
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