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Question: Is |X+1|<2? 1. (X-1)^2 < 12. X^2-2 < 0Source: GMAT Club Tests - hardest GMAT questions ____________________ Would someone please explain to me what the simplest way of solving this problem is? 1) From S1, is there a quick way to come to the conclusion that 0<x<2 2) From S2, is there a quick way to come to the conclusion that -2<X< square root of 2 3) When the question asks if |X+1|< 2, do we conclude that it is asking if X is either <1 OR <-3? Thank you.
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IMO A as (1) is SUFFICIENT from (1), we get 1<x<2 from (2), we get 0<x<1.414 dczuchta wrote: Would someone please explain to me what the simplest way of solving this problem is?
1) From S1, is there a quick way to come to the conclusion that 0<x<2
2) From S2, is there a quick way to come to the conclusion that -2<X< square root of 2
3) When the question asks if |X+1|< 2, do we conclude that it is asking if X is either <1 OR <-3?
Thank you,
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Question:
Is |X+1|<2?
1) (X-1)^2 < 1
2) X^2-2 < 0
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dczuchta wrote: Would someone please explain to me what the simplest way of solving this problem is?
1) From S1, is there a quick way to come to the conclusion that 0<x<2
2) From S2, is there a quick way to come to the conclusion that -2<X< square root of 2
3) When the question asks if |X+1|< 2, do we conclude that it is asking if X is either <1 OR >-3?
Thank you,
____________________
Question:
Is |X+1|<2?
1) (X-1)^2 < 1
2) X^2-2 < 0 1) From S1, is there a quick way to come to the conclusion that 0<x<2 (x-1)^2 < 1 (x-1) < 1 x < 2 (x-1) > -1 x > 0 sufff.... 2) From S2, is there a quick way to come to the conclusion that -2<X< square root of 2 x^2 - 2 < 0 x^2 < 2 x < sqrt2 or x > -sqrt2 insuff.......... 3) When the question asks if |X+1|< 2, do we conclude that it is asking if X is either <1 OR >-3? yes, |x+1|< 2 means -3< x <1. This is how it is solved: If |x+1| is +ve, (x+1) < 2. Or, x < 2-1 Or, x < 1 If |x+1| is -ve, -(x+1) < 2. Or, -(x+1) < 2. Or, -x-1 < 2. Or, -2-1 < x Or, -3 < x Hence -3 < x < 1.  If any typo, thats mine. 
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Re: m20 # 33 Kudos? [#permalink]
 12 Mar 2009, 11:03
Thank you. Makes sense. Looking at it now, I'm not even sure what I was confused about-maybe a wrong calculation. What happened to the Kudos?; the button seemed to have been deleted. 
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maybe I'm having a brainfart, but I think the answer is E (1) 0<x<2 (2) -sqrt(2)<x<sqrt(2) we need to know if -3<x<1 (1) and (2) tells us nothing that can be definite proof.
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Is |X+1|<2?
1. (X-1)^2 < 1
2. X^2-2 < 0
E.
We have to have -3 < x < 1
1. Consider x=1.1. (1.1-1)^2 = .1^2 = 0.01 (less than one) falls outside -3 < x < 1
Also consider 0.1. (0.1-1)^2 = (-0.5)^2 = .25 (less than one) falls inside -3 < x < 1
This is insuff because it can fall in and it can fall out of our -3 < x < 1.
2. Consider x = 1.1. 1.1^2 - 2 = 1.21 - 2 = (less than 0) falls outside -3 < x < 1
Also Consider x = 0.1. .1^2 - 2 = 0.01 - 2 = (less than 0) falls inside -3 < x < 1
This is insuff because it can fall in and it can fall out of our -3 < x < 1.
Also remember you aren't answering "Is |X+1|<2?". You are answering if 1 or 2 can answer that question.
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is |x+1|<2 can be rewritten as
x+1<2 or -x-1<2
x<1 or x>-3
1)(x-1)^2<1
(x-1)<1
x<2 so insufficient
2)x^2-2<0
x+\sqrt{2} x-\sqrt{2} <0
x+\sqrt{2} <0 or x-\sqrt{2}<0
x<-1.414 or x<1.414
so insufficient
combining both 1 and 2 x can still be 1.2 or 0.5 so both are also insufficient
so ans is E
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Ans is E
Q is if -3<X<1
1 gives 0<x<2
2 gives -sqroot(2) < X < sqroot(2)
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what is OA for me ANS is : E
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asimov wrote: maybe I'm having a brainfart, but I think the answer is E
(1) 0<x<2
(2) -sqrt(2)<x<sqrt(2)
we need to know if -3<x<1
(1) and (2) tells us nothing that can be definite proof. Absolutely right. So E is the answer.
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Yes E is the answer. Both statements 1 and 2 give us that X can be atleast 1 or 0. If X = 1 it fails and if X = 0 it passes the |X+1|^2 test. Hence data is not sufficient even with both.
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Its E.
Question: It becomes -3<x<1
1) Solving 1 says 0<x<2 Insufficient
2) Solving 2 says x< sqrt2 Insufficient
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|x+1| < 2 x + 1 < 2 or -x-1 < 2 x < 1 or x > -3 From (1) (x - 1)^2 < 1 x^2 -2x + 1 < 1 => x(x-2) < 0 So 0 < x < 2, so not enough From (2) -1.4 < x < 1.4, so not enough From (1) and (2) also, not enough as x can fall in 1 < x < 1.4, so answer is E.
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IMO E.
Both the conditions are not sufficient to conclude.
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Most authors agree that the stem asks if -3<x<1, me too.
However, since it seems that most posts struggle with the first statement, here is my take.
(1) states (x-1)2 < 1
If (x-1)2 < 1, then most would agree that (x-1)2 is also either equal or greater than 0, since squares cannot be negative.
0<= (x-1)2 < 1 is what needs to be solved.
(x-1)(x-1) < 1
x2 - 2x + 1 < 1
x2 - 2x < 0
x2 < 2x
At this point we can see that 0 < x <= 1, which makes this statement insufficient as x, per stem cannot be 1.
(2) x < sqrt2 or x > -sqrt2
(C) To analyze them together, we have to look at both.
0 < x <= 1
(-1.41) -sqrt2 < x < sqrt2 (1.41)
Here we can see, that 1 is still part of both, which makes this question E.
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dczuchta wrote: Question: Is |X+1|<2? 1. (X-1)^2 < 12. X^2-2 < 0Source: GMAT Club Tests - hardest GMAT questions ____________________ Would someone please explain to me what the simplest way of solving this problem is? 1) From S1, is there a quick way to come to the conclusion that 0<x<2 2) From S2, is there a quick way to come to the conclusion that -2<X< square root of 2 3) When the question asks if |X+1|< 2, do we conclude that it is asking if X is either <1 OR <-3? Thank you. let me know if my method is OKay...though it is learnt now only by going through the above observations and my own calculations 1) (x-1)sq < 1 (x-1) < + or - 1 so x-1 is between - 1 to +1 hence x is between 0 to 2 ( exclusive) so it can take the value 1 , then the solution gives YES if it takes 1.99, then the solution gives NO hence insufficient... A and D are gone 2) xsq - 2 < 0 xsq < 2 x is between -1.41 to + 1.41, so this also gives both YES and NO as answer so B is gone too answer should be b/w C and E taking together x would now be between o and 1.41 so here too we get YES and NO for the solution, hence E is the answer
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harshavmrg wrote: let me know if my method is OKay...though it is learnt now only by going through the above observations and my own calculations
1) (x-1)sq < 1
(x-1) < + or - 1
so x-1 is between - 1 to +1
hence x is between 0 to 2 ( exclusive)
so it can take the value 1 , then the solution gives YES
if it takes 1.99, then the solution gives NO
hence insufficient... A and D are gone
2) xsq - 2 < 0
xsq < 2
x is between -1.41 to + 1.41, so this also gives both YES and NO as answer
so B is gone too
answer should be b/w C and E
taking together
x would now be between o and 1.41
so here too we get YES and NO for the solution, hence E is the answer Yes, your solution is correct. Is |x+1|<2?Is |x+1|<2? --> is -3<x<1? (1) (x-1)^2 < 1 --> since both sides of the inequality are non-negative we can take square root from it: |x-1|<1 --> 0<x<2. Not sufficient. (2) x^2-2 < 0 --> x^2<2 --> again, since both sides of the inequality are non-negative we can take square root from it: |x|<1.4 (approximately) --> -1.4<x<1.4. Not sufficient. (1)+(2) Intersection of the ranges from (1) and (2) is 0<x<1.4. So, x could be in the range -3<x<1 (for example if x=1) as well as out of the range -3<x<1 (for example if x=1.2). Not sufficient. Answer: E.
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Complete solution of the problem,
Given in question stem,
|X+1|< 2
If, (X+1)< 0
-(X+1) < 2
X+1 > -2
X > -3
If(X+1) > 0
(X+1) > 2
X > 1
So we have to check that if any equation proves -3 < X < 1, that will be sufficient condition
I - (X -1)^2 < 1
(X -1 ) < 1 or (X - 1) > -1
On solving, 0 < X < 2
This is not sufficient condition, So A and D are incorrect choices.
II - X^2 -2 < 0
X^2 < 2
On solving, \sqrt{-2} < X < \sqrt{2}
This is not sufficient condition, So B and D are incorrect choices.
I and II together,
0 < X < \sqrt{2}
This is also not sufficient, so Ans is E
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