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

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21 Feb 2012, 22:07

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

(1) x < 0 (2) y < 1

I rephrased the original question as Is x<0? Statement 1 : SF Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x - X<0 or, - 0<X<0.5 Basis this II is insufficient.. Where am I going wrong ?

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.

Bunuel,why didn't i get it with the way i solved it? Am unable to understand where my approach is wrong . Thanks

You forgot that it's given that y=integer. (2) says y<1, thus |x|+x must also be some integer less than 1: 0, -1, ... but if you refer to my solution you'll see that |x|+x can never be negative, so the only valid solution for |x|+x (or which is the same for y) is 0.

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

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07 Jul 2013, 19:30

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

(1) x < 0

y = |x| + x y=-x+x y=0 SUFFICIENT

(2) y < 1 TRICKYYYYYY I originally said it was insufficient because it tells us nothing about the sign. However, if y is less than one and is an integer and it is equal to |x|+x then it must be zero!! SUFFICIENT

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

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07 Sep 2014, 02:25

devinawilliam83 wrote:

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

(1) x < 0 (2) y < 1

I rephrased the original question as Is x<0? Statement 1 : SF Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x - X<0 or, - 0<X<0.5 Basis this II is insufficient.. Where am I going wrong ?

point to remember is y is an integer

if y<1 , then y could be 0, -1, -2 and so on .. here according to the second condition if x= 0 then y= 0 , if x = -ve then Y = 0 , if x = +ive like 1 then second choice only will fail, if x = 0.5 then y cant be less than one, if x=.2 or .3 then y cant be integer.

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

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19 Jan 2015, 01:14

stat 1: X<0 => y = -x+x =0 suff stat 2:y is in integer & y<1 => y<=0 ...y can be less than zero only when x is less than zero => y = -x+x = 0 and for y=0...ntn to calculate suff => Ans D

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

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25 Feb 2016, 07:37

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