@anshu, that |x-3|=<-y and y<=0 doesn't mean that we have fixed condition for |x-3|=<0 - and even if we have there are still two solutions, one is interval x<3 and the other is x=3.
I approached this question differently.
st(1) |x-3|>=y, since y can be 0 OR +ve we get at least two values for x --> x=3 when x-3=0, and x>3 when when x-3>0;
st(2) |x-3|<= -y, -y can be -ve or 0 only, because y>=0. BUT if we square both parts we get (x-3)^2<=0 WHICH means (x-3) CAN be only 0 BUT not -ve, as the squared value cannot be -ve. Hence x-3=0 and x=3 Sufficient.
Choice B should be relevant here.
anshumishra wrote:ghoward199 wrote:From a GMAT CAT Practice Test:
If y>=0, what is the value of x?
I. lx-3l>=y
II. lx-3l<=-y
I am not sure why the correct answer is B.
y>= 0, x = ?
Statement 1:
|x-3| >=y , clearly x can have any value based on y's value - Insufficient
Statement 2:
|x-3| <= -y
Since mod of any value has non-negative value, hence |x-3| >=0
Also, y >=0 , hence -y <= 0
Therefore, |x-3| = 0 => x= 3 --- Sufficient,
B
