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Inequalities question

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Manager
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Inequalities question [#permalink] New post 25 Feb 2010, 02:39
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:22) correct 0% (00:00) wrong based on 15 sessions
abs(x) = absolute value of x

Image:
A number line with the values -5 to 3 highlighted (inclusive)

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
(A) abs(x) <= 3
(B) abs(x) <= 5
(C) abs(x-2) <= 3
(D) abs(x-1) <= 4
(E) abs(x+1) <= 4

OA:
[Reveal] Spoiler:
E


I (kind of) intuitively understand why that's the answer, but if I do it following the rules of inequalities I get B (in hindsight I can also see why that's wrong). HOW do I solve these without wasting too much time then?
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Re: Inequalities question [#permalink] New post 25 Feb 2010, 03:11
| x + 1 | <= 4

X has 2 possible values & you have to check both.

when X is positive :

X+1 <= 4 , so x <= 3

when X is negative :

X +1 => -4 ( sign reversed as if you multiplied by -1 )
so x => -5

-5 <= X <= 3. which is your number line
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Re: Inequalities question [#permalink] New post 25 Feb 2010, 04:55
Expert's post
1. length: 3-(-5) = 8. So, we should look for an inequality with 8/2=4 on right side. (D, E)

2. A center point is (3+(-5))/2= -1. So, we should look for x-(-1) = x+1 under modulus. It is E

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Re: Inequalities question [#permalink] New post 25 Feb 2010, 08:54
nickk wrote:
abs(x) = absolute value of x

Image:
A number line with the values -5 to 3 highlighted (inclusive)

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
(A) abs(x) <= 3
(B) abs(x) <= 5
(C) abs(x-2) <= 3
(D) abs(x-1) <= 4
(E) abs(x+1) <= 4

OA:
[Reveal] Spoiler:
E


I (kind of) intuitively understand why that's the answer, but if I do it following the rules of inequalities I get B (in hindsight I can also see why that's wrong). HOW do I solve these without wasting too much time then?


gmat OG q130 as mentioned in one earlier post also.

Answer is E, same explanation as og-12-problem-87647.html
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Re: Inequalities question [#permalink] New post 21 Nov 2011, 09:04
We need to find the center point in the shaded part of the number line.

Here it is easy to identify that -1 is the center point and the region is 4 units from it on either side.

So x is less than 4 units on either side of -1
this gives |x+1|<=4.

Ans: e
Re: Inequalities question   [#permalink] 21 Nov 2011, 09:04
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