Hi there,

I agree the explanation with elimiting the variable from the equation by making an assumption is very roundabout. Let me try explaning another way.

From the algebra you showed, we can reduce the eq to:

x(x-1) > y(y-4)

Now, let's go through the answer choices to find out which values of y satisfy the equation.


Starting with answer choice A, suppose y = 0. Then, x(x-1) > 0. Since our only restriction on x is that x > 0, it is perfectly valid to pick x = 1. However, in that case we get 0 > 0. Since that is not true, y = 0 does not satisfy this equation.

Moving on to asnwer choice B, let's say y > 0. Since y is an integer, this is equivalent to y >= 1. Thus, we get:

x(x-1) > y(y -4) >= -3.

Is it always true that x(x-1) >= -3?

Well, x > 0. Again, since it is an integer this means x >= 1. The smallest value of x(x-1) is thus 1(1-1) = 0.

So, when y > 0, we get 0 > -3. Since that is true, y > 0 satisfies the equation and our answer is B.

Hope this explanation made more sense,

Tatiana

Whats the source of this question, it doesn't look like much thought was put in while writing it:

it provides redundant information

1. X and Y are consecutive positive integers
2. x>0

then in the answers it provides option that are obviously contradicting the info in the stem

(a) y = or > than 0