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Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0

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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| > 0 [#permalink] New post 02 Nov 2012, 01:00
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himanshuhpr wrote:
Is |x| < 1?

(1) |x + 1| = 2|x - 1|
(2) |x - 3| > 0

From 1st statement we know that x = 1/3 or x= 3
From 2nd statement we know that that x>3 or x<3

My question is can we combine these 2 results and say (c) is sufficient as x>3 in statement creates an ambiguity and therfore it should be E.



(2) |x - 3| > 0. Absolute value is always more than or equal to zero. Thus this statement just says that |x - 3|\neq{0} --> x\neq{3}.

Hope it helps.
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 07 Jul 2013, 23:53
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 08 Jul 2013, 00:24
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yezz wrote:
Is |x| < 1?

(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0


Questions asks if -1<x<1

From St1 we can say that since both LHS and RHS is positive therefore squaring both sides we get

(x+1)^2= 4(x-1)^2
On simplifying we get 3x^2-10x-3= 0 -----> x=3 or x= 1/3

2 ans and hence st 1 is not sufficient. Therefore Option A and D ruled out

St 2 we have |x - 3| ≠ 0 and since Modulus of any no is greater than or equal to 0 (In this case greater than 0) which means x not equal to 3

Not sufficient.

Combining both equation we see that x=1/3 which is in the Question stem range

Ans C
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 08 Jul 2013, 15:27
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Is |x| < 1?

(1) |x + 1| = 2|x - 1|
(My first problem was to decide how to solve this. I had recently tackled a problem to the effect of |x-z|=|x-y| where I squared both sides to help simplify. In this case, it might be better to find the check points of the LHS and RHS as we are given a variable and an integer as opposed to all variables like the problem I had to solve before)
|x + 1| = 2|x - 1|
x=-1, x=1
so, x<-1, -1<x<1, x>1
x<-1:
-(x+1) = 2 -(x-1)
-x-1 = 2(-x+1)
-x-1 = -2x+2
x=3 INVALID as 3 does not fall within the range of x<-1

-1<x<1
(x+1) = 2 -(x-1)
x+1 = -2x+2
3x=1
x=1/3 VALID as x falls within the range of -1<x<1

x>1
(x+1)=2(x-1)
x+1=2x-2
-x=-3
x=3 VALID as x falls within the range of x>1

We have two valid values for x and therefore we cannot determine a single, correct answer.
INSUFFICIENT

(2) |x - 3| ≠ 0
Tells us nothing about the sign of x. x could be -10 or +10 and |x - 3| ≠ 0 would be valid.
INSUFFICIENT

1+2) x=1/3 OR x=3 AND |x - 3| ≠ 0

Plug in both x values into the above equation. x=3 fails as it does = 0 when the equation says it does not. Therefore, the only remaining x value is 1/3.
SUFFICIENT

(C)
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 03 Sep 2013, 05:27
From (1) Taking sqaure of both sides ((X+1)^2)/((X-1)^2 = 4, solving this you get X = 3 or 1/3, which is not sufficient.

(2) says X is not = 3

Hence both together tell us the answer (C)
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 03 Sep 2013, 05:54
I m really sorry, even after reading all the above replies.. i just could'nt get it..

Could someone point out to what i m missing out here..
As per my understanding |x| < 1 means -1 < x < 1 .. which eventually means is x=0 ?
Why do we have to consider the cases of x <-1 etc etc.. ?
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 03 Sep 2013, 05:58
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thinktank wrote:
I m really sorry, even after reading all the above replies.. i just could'nt get it..

Could someone point out to what i m missing out here..
As per my understanding |x| < 1 means -1 < x < 1 .. which eventually means is x=0 ?
Why do we have to consider the cases of x <-1 etc etc.. ?


Why does "is -1 < x < 1?" means "is x=0"? We are not told that x is an integer.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Is |x| < 1? [#permalink] New post 30 Jan 2014, 06:18
Economist wrote:
C

1)
if x>1, solving the equality we get x=3.
if -1<x<1, we get x=1/3.
if x<-1, we get x=3.

Not suff
2)
we get x is not equal to 3.

Combining, x can only be 1/3 :)
OA?


Actually your third range is wrong I believe. If x<-1 then x cannot be 3, it isn't a valid solution but the rest is OK

Cheers
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Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink] New post 05 Jul 2014, 00:21
This is very good question
X<-1
-x-1=2(-x+1)

-1<=x<=1
x+1=2(-x+1)

X>1
x+1=2(x-1)
Re: Is |x| < 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0   [#permalink] 05 Jul 2014, 00:21
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