DS - please explain

[calpol]

A, B, and P are positive integers, is P a product of 2 consecutive odd numbers?
1) P=4A^2-4B^2
2) B=1
[spoiler]
OA:A[/spoiler]

I am not sure how to derive the answer. Please explain.
Thanks!

[m&m]

let's rule out (B) since knowing what the variable b is doesn't help us solve for P without knowing the relationship of b to p.

in (A)
we have P=4A^2 - 4B^2 = 4(A^2 - B^2)

the question asks whether P = x*(x+1) = x^2 + x

now while A^2 = (B^2)^2 that would yield the form (B^2)^2 + B^2 the minus sign cannot co-exist with the consecutive integer criteria - so we can say B is sufficient to know that P cannot be product of consecutive integers

HOpe that helps

[mike22629]

I think you misread question MM. It asks if p is the product of two consecutive ODD integers.

We know that A,B,P are positive integers....

P = 4(A^2) - 4(B^2)

And even number times any odd number is always even; therefore both terms on the right side of the equation are even whether A or B are even or odd.

Furthermore, an even number minus an even number is always even.

The question asks if P is the product of two odd integers, which will always make it odd.

When can see that p will always be even thus making it impossible.

IMO A.