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Source: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?

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?

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.

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.
_________________

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.

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.
_________________

Source: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
_________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat