I agree that b must be true. However, if b is true, then A must also be true.

If y > 0, then it is also true that Y >= 0.

**Quote:**

That's not true. If y=0 and x=y+1=1, then \(x^2-1 \gt y^2-4y+x-1\) does NOT hold true.

This is a problem of semantics. I agree that Y cannot be 0.

What I say is that if Y is more than 0, then it must also be true that Y is more than -1 , or -2, or it is equal or more than 0.

If you give me any valid number for Y , answers Y>0 and y>= 0 are always true.[/quote]

**Quote:**

No, that's not correct.

The question asks: which of the following must be true?

A says \(y\geq{0}\), so it allows y to be 0. But y cannot be 0 because in this case \(x^2-1 \gt y^2-4y+x-1\) does NOT hold true. Thus A is not always true.

Of course 0 is not true. You must not test O (zero) because it is not a valid answer. What I said is that for any

valid integer of Y , y>0 is true, but also Y>=0 is true. This is what the the question asks for.

Let' see it as a sets problem. B is the set of all positive integers, and A is the set of all non-negative integers. This way A has the same elements of B, as well as the 0; therefore, any element that is in B is also in A.

B says that y>0, and that is true. A says that Y is equal

or more than 0. If Y is more than 0 -excluding 0- it means that Y>= 0 (more

or equal, one

or the other). We can even say that Y must be more than

-10, and it will be true. Y does not have to be 0 in order to be equal or more than 0.

Study the question carefully.

The question did not ask for all possible values of Y;

The question is: Is A true for all values of Y? The answer is

YESThe question

is not: : Is Y true for all values of A? The answer is

NOT
_________________

Clipper Ledgard

GMAT Coach