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

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Manager
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If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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14 Dec 2010, 22:03
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50% (01:21) correct 50% (01:11) wrong based on 501 sessions

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

(1) x < 0
(2) y < 1
Math Expert
Joined: 02 Sep 2009
Posts: 58443
If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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21 Feb 2012, 22:19
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Math Expert
Joined: 02 Sep 2009
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If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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15 Dec 2010, 01:50
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If y is an integer and y = |x| + x, is y = 0?

Notice that from $$y=|x|+x$$ it follows that y cannot be negative:
If $$x>0$$, then $$y=x+x=2x=2*positive=positive$$;
If $$x\leq{0}$$ (when x is negative or zero) then $$y=-x+x=0$$.

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

(2) $$y<1$$. We found out above that y cannot be negative and we are given that y is an integer, hence $$y=0$$. Sufficient.

Also discussed in Inequality and absolute value questions from my collection: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it's clear.
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Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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21 Feb 2012, 22:07
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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 ?
##### General Discussion
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Posts: 639
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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14 Dec 2010, 22:39
1
Each of (1) and (2) are sufficient to answer the question. Thus the answer should be "D".
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.

Yes it can definitely lead to the Zero.

You can plug and play certain values ( numbers ) in order to verify the above.
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Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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16 Dec 2010, 06:51
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.

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

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

A word of caution: When you read "If y is an integer and y=|x|+x", analyze it there and then. y can be a positive integer when x is positive, y will be 0 when x is negative and y will be 0 when x is 0."
Another important point to note here: When the author puts in extra effort to write "y is an integer" rather than "x and y are integers" , take special note that x may not be an integer. Not that it matters very much here but in many questions such a statement will have special significance.
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Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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21 Feb 2012, 22:43
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks
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Posts: 58443
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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21 Feb 2012, 23:35
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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Re: If y is an integer and y =|x| + x, is y =0? 1.x<0  [#permalink]

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17 Oct 2019, 02:57
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Re: If y is an integer and y =|x| + x, is y =0? 1.x<0   [#permalink] 17 Oct 2019, 02:57
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