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Modulus

by rahulvsd » Sat Apr 14, 2012 10:01 pm
Which of the following inequalities must be true for the value of x to be between -1 and 5?

A. |3 - x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x - 2| < 3

[spoiler]OA: E Source: GMAT Club Diagnostic Test[/spoiler]
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by sam2304 » Sat Apr 14, 2012 10:49 pm
rahulvsd wrote:Which of the following inequalities must be true for the value of x to be between -1 and 5?

A. |3 - x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x - 2| < 3

[spoiler]OA: E Source: GMAT Club Diagnostic Test[/spoiler]
Choose 3 values for these type of problems. one outside the left limit, one outside right limit and one within the limit.

Go with one within the limit first. say x = 1, we can see only 2nd and 5th option gets satisfied.
Now check for the outer limits with B and E, say x = -2, E doesn't gets satisfied
Take the right outer limit, x = 6, E doesn't gets satisfied.

IMO E.
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by Shalabh's Quants » Mon Apr 16, 2012 5:52 am
rahulvsd wrote:Which of the following inequalities must be true for the value of x to be between -1 and 5?

A. |3 - x| < -3
B. -1< |x| < 5
C. |x| - 2 > 2
D. |2 + x| > 3
E. |x - 2| < 3

[spoiler]OA: E Source: GMAT Club Diagnostic Test[/spoiler]
A. |3 - x| < -3 => 3-x<-3 or -x<-6 or x>6. Can't be ans.

B. -1< |x| < 5 => -1<x<5 or 1>x>-5. Taking both into consideration -1<x<1. Can't be ans.

C. |x| - 2 > 2 => |x|>4 => x>4 or x<-4. Can't be ans.

D. |2 + x| > 3 => 2+x>3 => x>1 or 2+x<-3 => x<-5. Can't be ans.

E. |x - 2| < 3 => x-2<3 => x<5 or x-2>-3 => x>-1 or -1<x<5. This is the ans.

Ans E.
Shalabh Jain,
e-GMAT Instructor
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