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

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Manager
Joined: 27 Aug 2014
Posts: 83

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

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11 Sep 2017, 06:55
Bunuel wrote:
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: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.

Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?

Kudos [?]: 2 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139663 [0], given: 12794

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

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11 Sep 2017, 06:58
sinhap07 wrote:
Bunuel wrote:
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: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.

Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?

Let me ask you: say x = -1. Knowing that x is negative do you change x there to -x and write -x = -1?
_________________

Kudos [?]: 139663 [0], given: 12794

Manager
Joined: 27 Aug 2014
Posts: 83

Kudos [?]: 2 [0], given: 3

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

### Show Tags

11 Sep 2017, 07:19
Bunuel wrote:
sinhap07 wrote:
Bunuel wrote:
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: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.

Hi Buneal

In stmt 1, we are given that x is negative. Then how does the second x remain positive. Should it not become -x-x=-2x ?

Let me ask you: say x = -1. Knowing that x is negative do you change x there to -x and write -x = -1?

Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?

Kudos [?]: 2 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139663 [0], given: 12794

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

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11 Sep 2017, 07:37
sinhap07 wrote:
Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?

That's totally wrong. A variable can stand for positive or negative number and you should not change it because you know its sign.
_________________

Kudos [?]: 139663 [0], given: 12794

Manager
Joined: 27 Aug 2014
Posts: 83

Kudos [?]: 2 [0], given: 3

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

### Show Tags

11 Sep 2017, 09:00
Bunuel wrote:
sinhap07 wrote:
Interesting point. No. That will be incorrect. But in algebra, we understand that a variable can take any sign ie positive or negative unless given explicit. So in stmt 1, is it that |x|+x is actually -x-(-x)?

That's totally wrong. A variable can stand for positive or negative number and you should not change it because you know its sign.

Thanks Bunuel. Guess I mixed it up for mod function.

Kudos [?]: 2 [0], given: 3

Re: If y is an integer and y = |x| + x, is y = 0?   [#permalink] 11 Sep 2017, 09:00

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