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

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VP
Joined: 23 Feb 2015
Posts: 1254
Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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10 Mar 2019, 09:52
2
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:20) correct 46% (01:27) wrong based on 69 sessions

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

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Senior Manager
Joined: 25 Feb 2019
Posts: 336
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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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

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7957
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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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 $$x+y^2<0....x<-y^2...x<0$$
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7957
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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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....
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Senior Manager
Joined: 25 Feb 2019
Posts: 336
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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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
SVP
Joined: 26 Mar 2013
Posts: 2343
Re: Is |x|+x>|x|? 1) x<y^2 2) x+y^2<0  [#permalink]

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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 $$x+y^2<0....x<-y^2...x<0$$

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