the condition |x â€“ 5| < 11?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Oct 18, 2011 1:39 am

How many numbers in the set {-8, -5, 0, 10, 20} satisfy the condition |x - 5| < 11?
(A) none
(B) one
(C) two
(D) three
(E) four

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Source: Beat The GMAT — Problem Solving | Tue Oct 18, 2011 1:39 am

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

by shankar.ashwin » Tue Oct 18, 2011 1:51 am

-5,0 and 10 satisfy the inequality. Hence D

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Oct 18, 2011 2:04 am

sanju09 wrote:How many numbers in the set {-8, -5, 0, 10, 20} satisfy the condition |x - 5| < 11?

One obvious solution is individual checking of each of the options.

Another approach is to utilize the concept of number line.
|x - 5| < 11 implies that the distance of x from 5 is less than 11.
Only -5, 0, and 10 lies within a distance of 11 from 5.

The correct answer is D.

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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 » Tue Oct 18, 2011 2:04 am

|x| < a implies -a<x<a , for example |x| < 2 x can be -1, 0 ,1 and any number between -2 and 2

So, |x - 5| < 11 ==> -11 < x-5 < 11 => adding 5 on all the sides -6 < x < 16. So, the numbers satisfying this condition are [spoiler]-5,0,10, i.e : Option D [/spoiler]

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Tue Oct 18, 2011 7:19 am

sanju09 wrote:How many numbers in the set {-8, -5, 0, 10, 20} satisfy the condition |x - 5| < 11?
(A) none
(B) one
(C) two
(D) three
(E) four

A matter of 10 seconds , just check with the elements of the set and U will find only 3 elements satisfying the condition as follows -

-5 , 0 and 10

So, answer is 3..

Abhishek

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