If y >= 0, what is the value of x?

[Harish Dorai]

If y >= 0, what is the value of x?

1) |x - 3| >= y

2) |x - 3| <= -y

I was confused by this question. It says y >=0 in the question and Statement(2) says |x - 3| <= -y.

[anadi]

You have mentioned the solution yourself,

1) Is insufficient, it gives a range of values till infinity. Both =ve and -ve side.

2) |x - 3| <= -y and y>=0. Here in any case y cannot be greater than 0 since left side is always +ve or 0. So the only solution is x=3 and y = 0.

Hence 2 alone is sufficient.

[Harish Dorai]

Great! B is the right answer.

[Guest]

Hi instructors,

Could you please expand on what you mean when you state that x must = 3 in statement 2?

Thank you

[Guest]

Can someone elaborate the solution?

[mbarshaik]

Lets take the first case.

|x - 3| >= y

Y>=0

so x = 3 or x > 3 or < 3..Not sufficient

Second case

|x - 3| <= -y

Multiply both sides by -1

- |x - 3| >= y
If x = 3 then y = 0

If you take any other value |x - 3| is positive so thsi will lead to LHS being negative and y cannot be < 0. So only x = 3 is the possibility.

[RonPurewal]

http://www.manhattangmat.com/forums/if- ... t2675.html