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C
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Difficulty:
85%
(hard)
Question Stats:
48% (02:14) correct
52%
(02:16)
wrong
based on 429
sessions
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Is |x + 1| + |x - 2| < 4 ?
(1) x is between -0.5 and 4
(2) x is between -2 and 2.5
(1) x is between -0.5 and 4
(2) x is between -2 and 2.5
I keep getting B, but the OA says its C.. Could anyone help me understand please?
Updated on: 16 May 2020, 08:33
Originally posted by GMATinsight on 16 May 2020, 06:52.
Last edited by GMATinsight on 16 May 2020, 08:33, edited 1 time in total.
Last edited by GMATinsight on 16 May 2020, 08:33, edited 1 time in total.
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cnsih1532
Question: Is |x + 1| + |x - 2| < 4 ?
Let's examine the expression |x + 1| + |x - 2| < 4
i.e. (Distance of x from -1) + (Distance of x from 2) is Less than 4
If x < -1
then, (-1-x)+(2-x) < 4
i.e. 2x > -3
i.e. x > -1.5
If x > 2
then, (x-(-1))+(x-2) < 4
i.e. 2x-1 < 4
i.e. x < 2.5
i.e. Value of x must be between -1.5 and 2.5
Question REPHRASED: Is -1.5 < x < 2.5?
Statement 1: x is between -0.5 and 4
Some values are between -1.5 and 2.5 but some may be outside such as 3.5 as well hence
NOT SUFFICIENT
Statement 2: x is between -2 and 2.5
Some values are between -1.5 and 2.5 but some may be outside such as -1.,75 as well hence
NOT SUFFICIENT
COmbining the statements
-0.5 < x < 2.5
SUFFICIENT
Answer: Option C
General Discussion
16 May 2020, 07:09
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lx+1l + lx-2l <4?
if,x>=2 ,
x+1+x-2<4
or,2x<5
or,x<2.5
so,2≤x<2.5[/b]
if,-1<x<2
x+1+2-x<4
or,3<4 (always true)
if,x<=-1
-x-1+2-x<4
or,-2x<3
or,x>-1.5
so,-1.5<x≤-1
so, question asks if 2<=x<2.5 or -1<x<2 or -1.5<x<=-1
OR simply , -1.5<x<2.5?
1) x is between -0.5 and 4
if, x lies between -0.5 to 2.5 (x=1) ans is YES but if it lies between 2.5 to 4 ans is no (x=3) insufficient
2) x is between -2 and 2.5
if, x=1 ans is YES but x=-1.7 ans is no insufficient
combining 1 and 2
x is between -0.5 and 2.5
ans is always true. sufficient
correct answer C
if,x>=2 ,
x+1+x-2<4
or,2x<5
or,x<2.5
so,2≤x<2.5[/b]
if,-1<x<2
x+1+2-x<4
or,3<4 (always true)
if,x<=-1
-x-1+2-x<4
or,-2x<3
or,x>-1.5
so,-1.5<x≤-1
so, question asks if 2<=x<2.5 or -1<x<2 or -1.5<x<=-1
OR simply , -1.5<x<2.5?
1) x is between -0.5 and 4
if, x lies between -0.5 to 2.5 (x=1) ans is YES but if it lies between 2.5 to 4 ans is no (x=3) insufficient
2) x is between -2 and 2.5
if, x=1 ans is YES but x=-1.7 ans is no insufficient
combining 1 and 2
x is between -0.5 and 2.5
ans is always true. sufficient
correct answer C
