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the condition |x – 5| < 11?

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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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by shankar.ashwin » Tue Oct 18, 2011 1:51 am
-5,0 and 10 satisfy the inequality. Hence D
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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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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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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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