Is x 0? (1) |3 - x|

Question

Is x > 0?

(1) |3 - x| < |x + 5|
(2) |3 - 2x| < x - 1

Source: Experts Global

chetan2u · Answer

1....|3-x|<|x+5| Square both sides 9+x^2-6x-16....x>-1 x can be -0.5 or 0......Ans NO x can be 1,2,3.... Ans YES Insufficient 2..|3-2x|0...x>1 Suff B

Kurtosis · Answer

St1: |3 - x| < |x + 5|
Square on both sides: 9 + x^2 - 6x < x^2 + 25 + 10x --> x > -1
Not Sufficient

St2: |3 - 2x| < x - 1
3 - 2x < x - 1 --> x > 4/3
3 - 2x > 1 - x --> x < 2
4/3 < x < 2
Hence x > 0
Sufficient

Answer: B

niks18 · Answer

Statement 1: |3-x|<|x+5| , square both sides to get 9+x^2-6x16x>-16 =>x>-1 . Hence x>0 or x<0 . Insufficient Statement 2: implies -(x-1)<3-2x3-2x3x>4 =>x>\frac{4}{3} and 3-2x>1-x =>x<2 So range \frac{4}{3}0 . Sufficient Option B

Mo2men · Answer

Another approach (1) |3 - x| < |x + 5| I spotted quickly the following: Let x = 0 ......|3| < |5|..Answer is No Let x =1 .......|2| < |6|..Answer is Yes Insufficient |3 - 2x| < x - 1 |3 - 2x| is equal or greater than zero.......x-1 is also equal or greater than zero x -1 > 0...x >1>0 Sufficient Answer: B

utopian25 · Answer

For statement 1, how do we know that we need to square both side ? I was trying to solve it and could not get the answer. 
any tips on identifying this.

niks18 · Answer

Hi  adityanahan

by squaring a mod function you can get rid of the mod and then it becomes a simple equation which is easier to work with.
when you remove the mod function, then you need to be careful that you test both the positive and negative values. but by squaring, you can turn the function to a positive value as square is always positive or 0

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Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1

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