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

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If y is an integer and y = x + |x|, is y = 0? (1) x < 0 [#permalink]

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08 Aug 2011, 03:37
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Difficulty:

55% (hard)

Question Stats:

54% (00:15) correct 46% (00:19) wrong based on 26 sessions

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

I do not agree with OA.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-y-is-an-i ... 27927.html
[Reveal] Spoiler: OA

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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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08 Aug 2011, 03:53
suraabhi wrote:
If y is an integer and y = x + |x|, is y = 0?
(1) x < 0
(2) y < 1

I do not agree with OA.

We can conclude with sureness that "y=0" using each statement alone. OA is correct. Why do you think otherwise?
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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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08 Aug 2011, 03:58
Why is y not considered in negative range of Integers is what i am confused about.

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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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08 Aug 2011, 04:03
suraabhi wrote:
Why is y not considered in negative range of Integers is what i am confused about.

Because "y" can't be negative.

y = x + |x|

If x>0
y=x+x=2x
y=2x ; as x>0; y must be positive

If x<=0
y=x-x=0; Here y=0 for all x<=0;

In any case; y is either "0" or +ve.

1. x<0
y=0 for x<=0
Sufficient.

2. y<1;
The only non-negative integer less than 1 is 0.
Sufficient.

Ans: "D"
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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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08 Aug 2011, 04:56
Thanks fluke. Got it.

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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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08 Aug 2011, 05:38
fluke wrote:

Because "y" can't be negative.
y = x + |x|

If x>0
y=x+x=2x
y=2x ; as x>0; y must be positive

If x<=0
y=x-x=0; Here y=0 for all x<=0;

In any case; y is either "0" or +ve.

Fluke, Thanks.. I missed actually part where y has to be positive. Though got the answer right.
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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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08 Aug 2011, 16:22
[quote="suraabhi"]If y is an integer and y = x + |x|, is y = 0?
(1) x < 0
(2) y < 1

for y to be zero x has to be -ve

from 1
suff

from 2
not relevent

A

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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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09 Aug 2011, 19:09
suraabhi wrote:
If y is an integer and y = x + |x|, is y = 0?
(1) x < 0
(2) y < 1

I do not agree with OA.

Also go with D.

Remember ----- y is an integer.

1. If x is an integer and smaller than 0, then it is a -ve integer. When putting the value of x in the equation (y = x + |x|), y is always 0. Sufficient.

2. If y is smaller than 1, it must be 0 because no matter the value of x, the minimum (x + |x|) can be is 0. Sufficient.

(Here somebody might wonder y could be 2 if x = 1. But again, remember statement 2 says y<1 i.e y cannot be greater than 1. Therefore x also cannot be >0.)

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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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11 Dec 2017, 02:17
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-y-is-an-i ... 27927.html
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Re: If y is an integer and y = x + |x|, is y = 0? (1) x < 0   [#permalink] 11 Dec 2017, 02:17
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