It is currently 24 Jun 2017, 22:30

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# OG 12.problem 130

Author Message
Manager
Joined: 24 Aug 2009
Posts: 149

### Show Tags

05 Dec 2009, 15:20
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

100% (02:03) correct 0% (00:00) wrong based on 11 sessions

### HideShow timer Statistics

–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3)
130. Which of the following inequalities is an algebraic
expression for the shaded part of the number line
above?
(A) |x| ≤ 3
(B) |x| ≤ 5
(C) |x − 2| ≤ 3
(D) |x − 1| ≤ 4
(E) |x + 1| ≤ 4

The answer is E, why not B?
VP
Joined: 05 Mar 2008
Posts: 1469

### Show Tags

05 Dec 2009, 15:34
ISBtarget wrote:
–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3)
130. Which of the following inequalities is an algebraic
expression for the shaded part of the number line
above?
(A) |x| ≤ 3
(B) |x| ≤ 5
(C) |x − 2| ≤ 3
(D) |x − 1| ≤ 4
(E) |x + 1| ≤ 4

The answer is E, why not B?

b is saying -5≤x≤5
e is saying -5≤x≤3
x+1≤4 = x≤3
-x -1 ≤ 4
-x ≤ 5
x>=-5
Senior Manager
Joined: 23 May 2008
Posts: 414

### Show Tags

06 Dec 2009, 07:29
take both conditions
if x>0
ie. if x+1>0
or x>-1

then |x+1|<=4
x+1<= 4
x<= 3

If x<0
i.e if x+1<0
or x<-1

then -|x+1|<=4
-x-1<= 4
-x<= 5
x>= -5

combining the limits we get
-5<x<3 therefore E
Manager
Joined: 18 Feb 2010
Posts: 170
Schools: ISB

### Show Tags

22 Feb 2010, 01:16
ISB target ....try and put x=4 in eqn 2. It still holds good but doesnt satisfies your number options for the line. Eqn 5 does that for x=4 and is justified only for the numbers given in the quesn.

Hope its clear now.
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Senior Manager
Joined: 01 Feb 2010
Posts: 264

### Show Tags

22 Feb 2010, 07:49
ISBtarget wrote:
–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3)
130. Which of the following inequalities is an algebraic
expression for the shaded part of the number line
above?
(A) |x| ≤ 3
(B) |x| ≤ 5
(C) |x − 2| ≤ 3
(D) |x − 1| ≤ 4
(E) |x + 1| ≤ 4

The answer is E, why not B?

Length = 3-(-5) = 8
center = (-5)+8/2 = -1
Now only D & E has 8/2 = 4 on right side.
Also at x=-5 only E is satisfied and not D so answer is E.
Manager
Joined: 26 May 2005
Posts: 207

### Show Tags

22 Feb 2010, 08:39
|x+a| <= b

you can take the above case and simplify as below
if the origin is at (-a,0) then x will have as many values to the right of -a as to the left of -a. Bacially the values of x are symetric at the value (-a,0)

for the expression given in the question, the values of x are -5<=x<=3 .. the values are symetric at x=-1

so the expression would be a = 1 and b =4 ... |x+1|<=4
Intern
Joined: 26 Sep 2009
Posts: 9

### Show Tags

26 Feb 2010, 14:40
|x + 1| ≤ 4

remove the absolute value by

-4 ≤ x+1 ≤ 4

-1 -4 ≤ x+1 -1 ≤ 4 -1

-5 ≤ x ≤ 3
Intern
Joined: 26 Oct 2009
Posts: 7

### Show Tags

01 Mar 2010, 01:28

E is correct.
Manager
Joined: 05 Oct 2011
Posts: 171

### Show Tags

21 Nov 2011, 10:06
1
KUDOS

But if we were to solve directly from question to get the answer,
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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

### Show Tags

23 Nov 2011, 06:07
1
KUDOS
Expert's post
Check out this post. It discusses the visual approach of handling mods. Once you understand it, you can answer this question in 10 secs.
http://www.veritasprep.com/blog/2011/01 ... edore-did/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 08 Sep 2011
Posts: 71
Concentration: Finance, Strategy

### Show Tags

23 Nov 2011, 09:13
E. It is not B because B implies that it could be 4 or 5 as well when we know that it 3 is the highest positive number
Re: OG 12.problem 130   [#permalink] 23 Nov 2011, 09:13
Display posts from previous: Sort by