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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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New post 08 Aug 2011, 03:37
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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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New post 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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New post 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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New post 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
We have already seen this.
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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New post 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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New post 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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New post 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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New post 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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New post 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.

Answer: D.


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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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