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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.

Thus Answer should be D.

You can plug and play certain values ( numbers ) in order to verify the above.

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

If y is an integer and y = |x| + x, is y = 0? (1) x < 0 (2) y < 1

Note: as \(y=|x|+x\) then \(y\) is never negative. If \(x>{0}\) then \(y=x+x=2x>0\) and 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) \(y<1\), as we concluded y is never negative, and we are given that \(y\) is an integer, hence \(y=0\). Sufficient.

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. _________________

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

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06 Feb 2014, 04:45

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

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07 Feb 2014, 17:23

If y is an integer and y = |x| + x, is y = 0? y = 0, when x < 0; y = 2x, when x >=0 (1) x < 0 => y = 0 (2) y < 1 -> Because y is an integer, y has to be zero (y cannot be a negative integer because the least value of y is zero).

D

gmatclubot

Re: If y is an integer and y=|x|+x, is y=0?
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07 Feb 2014, 17:23

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