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# If y is an integer and y = |x| + x, is y = 0?

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Current Student
Joined: 25 Aug 2011
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Kudos [?]: 126 [1] , given: 11

If y is an integer and y = |x| + x, is y = 0? [#permalink]  21 Feb 2012, 21:07
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Difficulty:

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Question Stats:

43% (01:51) correct 57% (00:43) wrong based on 264 sessions
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0
(2) y < 1

I rephrased the original question as Is x<0?
Statement 1 : SF
Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
- X<0 or,
- 0<X<0.5
Basis this II is insufficient.. Where am I going wrong ?
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41035 [6] , given: 5654

Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]  21 Feb 2012, 21:19
6
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Expert's post
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2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

Notice that since $$y=|x|+x$$ then $$y$$ is never negative. If $$x>{0}$$ (so if x is positive) then $$y=x+x=2x$$ and for $$x\leq{0}$$ then (when x is negative or zero) then $$y=-x+x=0$$.

(1) $$x<0$$ --> $$y=|x|+x=-x+x=0$$. Sufficient.

(2) $$y<1$$, as we concluded y is never negative, and we are given that $$y$$ is an integer, hence $$y=0$$. Sufficient.

For hard inequality and absolute value questions with detailed solutions check this: inequality-and-absolute-value-questions-from-my-collection-86939-40.html

Hope it helps.
_________________
Current Student
Joined: 25 Aug 2011
Posts: 195
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Followers: 1

Kudos [?]: 126 [0], given: 11

Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]  21 Feb 2012, 21:43
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41035 [0], given: 5654

Re: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 [#permalink]  21 Feb 2012, 22:35
Expert's post
devinawilliam83 wrote:
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks

You forgot that it's given that y=integer. (2) says y<1, thus |x|+x must also be some integer less than 1: 0, -1, ... but if you refer to my solution you'll see that |x|+x can never be negative, so the only valid solution for |x|+x (or which is the same for y) is 0.

Hope it's clear.
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Math Expert
Joined: 02 Sep 2009
Posts: 27215
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Kudos [?]: 41035 [0], given: 5654

Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]  04 Jul 2013, 00:24
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________
Senior Manager
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]  07 Jul 2013, 18:30
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0

y = |x| + x
y=-x+x
y=0
SUFFICIENT

(2) y < 1
TRICKYYYYYY
I originally said it was insufficient because it tells us nothing about the sign. However, if y is less than one and is an integer and it is equal to |x|+x then it must be zero!!
SUFFICIENT

(D)
Manager
Joined: 07 Apr 2014
Posts: 148
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Kudos [?]: 10 [0], given: 81

Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]  07 Sep 2014, 01:25
devinawilliam83 wrote:
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0
(2) y < 1

I rephrased the original question as Is x<0?
Statement 1 : SF
Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
- X<0 or,
- 0<X<0.5
Basis this II is insufficient.. Where am I going wrong ?

point to remember is y is an integer

if y<1 , then y could be 0, -1, -2 and so on .. here according to the second condition if x= 0 then y= 0 , if x = -ve then Y = 0 , if x = +ive like 1 then second choice only will fail, if x = 0.5 then y cant be less than one, if x=.2 or .3 then y cant be integer.
Intern
Joined: 26 Mar 2013
Posts: 23
Location: India
Concentration: Finance, Strategy
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Kudos [?]: 8 [0], given: 2

Re: If y is an integer and y = |x| + x, is y = 0? [#permalink]  19 Jan 2015, 00:14
stat 1: X<0 => y = -x+x =0
suff
stat 2:y is in integer & y<1 => y<=0 ...y can be less than zero only when x is less than zero => y = -x+x = 0 and for y=0...ntn to calculate
suff
=> Ans D
Re: If y is an integer and y = |x| + x, is y = 0?   [#permalink] 19 Jan 2015, 00:14
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