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Gmat paper set Q

by gmat25 » Wed Jul 20, 2011 11:05 am
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0


OA given is Op C, i solved this question and i find out that for -1<x<0 in Op A we are getting x = 1/3, now this means that x cannot take any value b/w -1<x<0....while the question is (when u rephrase the question)

IS -1 < X < 1 ???....so clearly from above we get, x is b/w 0 and 1 but not b/w -1 and 0 so...i think the answer should be Op E not Op C....m i going somewhere wrong??? Please explain???
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Jul 20, 2011 1:42 pm
gmat25 wrote:Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0


OA given is Op C, i solved this question and i find out that for -1<x<0 in Op A we are getting x = 1/3, now this means that x cannot take any value b/w -1<x<0....while the question is (when u rephrase the question)

IS -1 < X < 1 ???....so clearly from above we get, x is b/w 0 and 1 but not b/w -1 and 0 so...i think the answer should be Op E not Op C....m i going somewhere wrong??? Please explain???
Statement 1: |x + 1| = 2|x - 1|
This means x+1 = 2(x-1) OR x+1 = -2(x-1).

Case 1:
x+1 = 2(x-1)
x+1 = 2x - 2
x=3.

Case 2:
x+1 = -2(x-1)
x+1 = -2x + 2
3x = 1
x = 1/3.

Since it's possible that x=3 and that x=1/3, we can't determine whether |x|<1.
Insufficient.

Statement 2: |x-3| ≠ 0
Thus, x ≠ 3.
Since x can be any value other than 3, insufficient.

Statement 1 and 2 combined:
From statement 1: x=3 or x =1/3.
From statement 2: x ≠ 3
Thus, the only value that satisfies both statements is x=1/3.
Sufficient.

The correct answer is C.
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by GAMATO » Wed Jul 20, 2011 2:02 pm
GMATGuruNY wrote:
gmat25 wrote:Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0


OA given is Op C, i solved this question and i find out that for -1<x<0 in Op A we are getting x = 1/3, now this means that x cannot take any value b/w -1<x<0....while the question is (when u rephrase the question)

IS -1 < X < 1 ???....so clearly from above we get, x is b/w 0 and 1 but not b/w -1 and 0 so...i think the answer should be Op E not Op C....m i going somewhere wrong??? Please explain???
Statement 1: |x + 1| = 2|x - 1|
This means x+1 = 2(x-1) OR x+1 = -2(x-1).

Case 1:
x+1 = 2(x-1)
x+1 = 2x - 2
x=3.

Case 2:
x+1 = -2(x-1)
x+1 = -2x + 2
3x = 1
x = 1/3.

Since it's possible that x=3 and that x=1/3, we can't determine whether |x|<1.
Insufficient.

Statement 2: |x-3| ≠ 0
Thus, x ≠ 3.
Since x can be any value other than 3, insufficient.

Statement 1 and 2 combined:
From statement 1: x=3 or x =1/3.
From statement 2: x ≠ 3
Thus, the only value that satisfies both statements is x=1/3.
Sufficient.

The correct answer is C.
Hi,

Can you please explain how you got x+1 = 2(x-1) OR x+1 = -2(x-1).

Can we ignore absolute value signs on the right hand side of the equation. In other words, are both the below equations identical?
|x + 1| = 2|x - 1| and
|x + 1| = 2(x - 1)
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by amit2k9 » Thu Jul 21, 2011 3:17 am
question is asking for -1 < x < 1 ?

a sign changing points are x= -1 and x = 1.

thus, x< -1 -(x+1) = -2(x-1) giving x=3. not a solution.

for, -1<x<1 (x+1) = -2(x-1) giving x=1/3. a solution.

for, x> 1 (x+1) = 2(x-1) giving x =3. a solution.

thus not sufficient.

b. x # 3. not sufficient.

a+b means x = 1/3. hence sufficient.

C it is.
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by gmat25 » Thu Jul 21, 2011 4:17 am
GMATGuruNY wrote:
gmat25 wrote:Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0


OA given is Op C, i solved this question and i find out that for -1<x<0 in Op A we are getting x = 1/3, now this means that x cannot take any value b/w -1<x<0....while the question is (when u rephrase the question)

IS -1 < X < 1 ???....so clearly from above we get, x is b/w 0 and 1 but not b/w -1 and 0 so...i think the answer should be Op E not Op C....m i going somewhere wrong??? Please explain???
Statement 1: |x + 1| = 2|x - 1|
This means x+1 = 2(x-1) OR x+1 = -2(x-1).

Case 1:
x+1 = 2(x-1)
x+1 = 2x - 2
x=3.

Case 2:
x+1 = -2(x-1)
x+1 = -2x + 2
3x = 1
x = 1/3.

Since it's possible that x=3 and that x=1/3, we can't determine whether |x|<1.
Insufficient.

Statement 2: |x-3| ≠ 0
Thus, x ≠ 3.
Since x can be any value other than 3, insufficient.

Statement 1 and 2 combined:
From statement 1: x=3 or x =1/3.
From statement 2: x ≠ 3
Thus, the only value that satisfies both statements is x=1/3.
Sufficient.

The correct answer is C.
Thanks a lot Mitch!!!

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https://www.beatthegmat.com/gmat-paper-s ... 87603.html
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