Data Sufficiency

This is a difficult one.....Pls provide explanation

Hi karthikpandian19:

I explained the other one you posted using the concept. That should make it easy to do this one.
I am going to try to do this one while typing. Let's see how it goes.

We have |a-2|

First we have

1) a<2 which means a-2<0; then |a-2| = - (a-2) = 2-a ; clearly not sufficient.

2) a+ b^2 = c^3 + 2
=> b^2 - c^3 = 2 - a ; again not sufficient since we don't know whether |a-2| is positive or negative.
Let's try together, from the first one we know that |a-2| = 2-a; clearly that tells us whether this is true (it is). Hence the answer is C .

Again the concept i have used is that if x<0 ; |x| = -x.

Let me know if this helps