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

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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27 Dec 2017, 10:16
1
4
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:29) correct 46% (02:19) wrong based on 112 sessions

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Is x > 0?

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

Source: Experts Global

_________________

You've got what it takes, but it will take everything you've got

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Joined: 02 Aug 2009
Posts: 7199
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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27 Dec 2017, 18:02
pushpitkc wrote:
Is x > 0?

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

Source: Experts Global

1....|3-x|<|x+5|
Square both sides
$$9+x^2-6x<x^2+25+10x....16x>-16....x>-1$$
x can be -0.5 or 0......Ans NO
x can be 1,2,3.... Ans YES
Insufficient

2..|3-2x|<x-1
Now |3-2x| will always be positive or 0, so x-1>0...x>1
Suff

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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27 Dec 2017, 18:10
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

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31 Dec 2017, 07:11
ashikaverma13 wrote:
Is x > 0?

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

Statement 1: $$|3-x|<|x+5|$$, square both sides to get

$$9+x^2-6x<x^2+25+10x$$

$$=>16x>-16 =>x>-1$$. Hence $$x>0$$ or $$x<0$$. Insufficient

Statement 2: implies $$-(x-1)<3-2x<x-1$$

$$=>3-2x<x-1 =>3x>4 =>x>\frac{4}{3}$$

and $$3-2x>1-x =>x<2$$

So range $$\frac{4}{3}<x<2$$. Clearly $$x>0$$. Sufficient

Option B
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Joined: 26 Mar 2013
Posts: 1998
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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01 Jan 2018, 02:00
pushpitkc wrote:
Is x > 0?

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

Source: Experts Global

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

Intern
Joined: 03 Nov 2017
Posts: 12
GMAT 1: 590 Q48 V23
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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07 Jan 2018, 09:17
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.
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Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1  [#permalink]

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07 Jan 2018, 09:48
2
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.

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
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 &nbs [#permalink] 07 Jan 2018, 09:48
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