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

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

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New post 11 Sep 2017, 07:55
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.

Answer: D.

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

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New post 11 Sep 2017, 07:58
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.

Answer: D.

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

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New post 11 Sep 2017, 08:19
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.

Answer: D.

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

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New post 11 Sep 2017, 08:37
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Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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New post 11 Sep 2017, 10:00
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.
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Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

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Re: If y is an integer and y = |x| + x, is y = 0?   [#permalink] 17 Sep 2018, 05:01

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