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Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0

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Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 09:52
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Difficulty:

  35% (medium)

Question Stats:

69% (01:18) correct 31% (00:58) wrong based on 26 sessions

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Is \(|x|+x>|x|\)?
1) \(x<y^2\)
2) \(x+y^2<0\)

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Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 10:02
statement 1

x is always positive so the the answer is yes .

statement 2 .

x is negative , then

the answer is always No .



IMO D .

each one is sufficient

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Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 10:06
Is \(|x|+x>|x|\)?
Now |x| is not negative, so subtract it from both sides without changing the inequality sign..=> the question becomes ' Is x>0?'
1) \(x<y^2\)
x can be both negative and positive.. say y=2 and x = -1, or y=2 and x=1...Insufficient
2) \(x+y^2<0\)
\(y^2\) will be 0 at the least so x<0 OR \(x+y^2<0....x<-y^2...x<0\)
The answer is NO...Sufficient
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 10:06
m1033512 wrote:
statement 1

x is always positive so the the answer is yes .

statement 2 .

x is negative , then

the answer is always No .



IMO D .

each one is sufficient

Posted from my mobile device


Check statement 1....
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 10:13
chetan2u wrote:
m1033512 wrote:
statement 1

x is always positive so the the answer is yes .

statement 2 .

x is negative , then

the answer is always No .



IMO D .

each one is sufficient

Posted from my mobile device


Check statement 1....


Thanks Chetan ,

x < y^2 , so x can be negative also,

I wrongly assumed x can not be negative
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Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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New post 10 Mar 2019, 10:19
chetan2u wrote:
Is \(|x|+x>|x|\)?
Now |x| is not negative, so subtract it from both sides without changing the inequality sign..=> the question becomes ' Is x>0?'
1) \(x<y^2\)
x can be both negative and positive.. say y=2 and x = -1, or y=2 and x=1...Insufficient
2) \(x+y^2<0\)
\(y^2\) will be 0 at the least so x<0 OR \(x+y^2<0....x<-y^2...x<0\)
The answer is NO...Sufficient


In Statement 1, x could be zero as well.
GMAT Club Bot
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0   [#permalink] 10 Mar 2019, 10:19
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