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25 Sep 2023, 20:24
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Asked: If ||x+3| - 12| < 13, what is the range of x?
-13 < |x+3| - 12 < 13
Case 1: |x+3| - 12 < 13
|x+3| < 25
-25 < x+3 < 25
-28 < x < 22
Case 2: -13 < |x+3| - 12
|x+3| > -1
Which is always true since |x+3| > 0 > -1
IMO C
-13 < |x+3| - 12 < 13
Case 1: |x+3| - 12 < 13
|x+3| < 25
-25 < x+3 < 25
-28 < x < 22
Case 2: -13 < |x+3| - 12
|x+3| > -1
Which is always true since |x+3| > 0 > -1
IMO C
26 Sep 2024, 18:40
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We can also solve such questions using the answer choices. Above is an example.
---
Harsha
GMAT Tutor | gmatanchor.com
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29 Sep 2024, 04:41
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||x+3| -12| < 13
assume |x+3| = a
|a-12| < 13
for a<12
-a+12 <13
-a <1
a>-1
|x+3| > -1
for x<-3
-x-3 >-1
-x > 2
x < -2
that means x<-3
OR
for x>-3
x+3 > -1
x>-4
that means x>-3
for a > 12
a-12 < 13
a < 25
|x+3| < 25
for x<-3
-x-3 <25
-x < 28
x>-28
-28<x<-3
for x >-3
x+3 <25
x<22
-3<x<22
therefore range is -28<x<22
combining all we get
-28<x<22
assume |x+3| = a
|a-12| < 13
for a<12
-a+12 <13
-a <1
a>-1
|x+3| > -1
for x<-3
-x-3 >-1
-x > 2
x < -2
that means x<-3
OR
for x>-3
x+3 > -1
x>-4
that means x>-3
for a > 12
a-12 < 13
a < 25
|x+3| < 25
for x<-3
-x-3 <25
-x < 28
x>-28
-28<x<-3
for x >-3
x+3 <25
x<22
-3<x<22
therefore range is -28<x<22
combining all we get
-28<x<22
