Inequalities

[treker]

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

I do not understand why the solution is D.
It is obvious that 1) is SUF, but what about 2)?

[Brent@GMATPrepNow]

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

I do not understand why the solution is D.
It is obvious that 1) is SUF, but what about 2)?

We can see that, if x is positive, then |x|+x will equal zero.
If x is positive, then |x|+x will have a positive value.
So, if x is negative, y is zero. If x is positive then y is positive. In other words, y is either a positive number or it is zero.
(2) tells us that y<1. Since y is an integer, y must equal 0. So, (2) is sufficient.

[heshamelaziry]

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

I do not understand why the solution is D.
It is obvious that 1) is SUF, but what about 2)?

We can see that, if x is positive, then |x|+x will equal zero.
If x is positive, then |x|+x will have a positive value.
So, if x is negative, y is zero. If x is positive then y is positive. In other words, y is either a positive number or it is zero.
(2) tells us that y<1. Since y is an integer, y must equal 0. So, (2) is sufficient.

Isn't -1 an integer ?

[viju9162]

yes, he hasn't told as +ve integers.. negative numbers can also be considered ..

[fruti_yum]

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

I do not understand why the solution is D.
It is obvious that 1) is SUF, but what about 2)?

We can see that, if x is positive, then |x|+x will equal zero.
If x is positive, then |x|+x will have a positive value.
So, if x is negative, y is zero. If x is positive then y is positive. In other words, y is either a positive number or it is zero.
(2) tells us that y<1. Since y is an integer, y must equal 0. So, (2) is sufficient.

I think that since y<1... y can be any number.. how is it that y is necessarily 0.. y can be -5 for all you know.. therefore Statement 2 is not sufficient.

[jiteshch]

Statement is not sufficient as per my understanding...
!!!
and statement 1 is sufficent as the question is y=2x for any value x<0 we can answer for sure that y is not 0.

Statement 2 ..y<1 y can be negative also so how it is sufficent ?????

Should Be A also is sufficent.. !!

[crackgmat007]

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

I do not understand why the solution is D.
It is obvious that 1) is SUF, but what about 2)?

A for me. If the question were to state that x is an integer, then my answer would be D.

[GMATQuantCoach]

2) Consider two cases: x>=0 and x<0.

If x>=0, then y = |x| + x = x + x = 2x.
That implies y >=0 because x>=0. y is an integer such that 0 <= y < 1. y can only be 0.

If x < 0, then y = |x| + x = -x + x = 0.

In both cases y = 0. That means no matter what x values you pick, y is equal to 0. Sufficient.