Is the positive integer p even?
(1) p^2 + p is even.
(2) 4p + 2 is even.
I answered A because any number that is squared, then added to itself and results in an even number MUST be even. The correct answer seems to have been E because, and I quote
"p^2 + p can be factored, resulting in p(p + 1). This expression equals the product of two consecutive integers and we are told that this product is even. In order to make the product even, either p or p + 1 must be even, so p(p + 1) will be even regardless of whether p is odd or even. Alternatively, we can try numbers. For p = 2, 2(2 + 1) = 6. For p = 3, 3(3 + 1) = 12. So, when p(p + 1) is even, p can be even or odd."
I don't fully understand how this expression was factored and moreover, if I take the two cases the explanation laid out, 2 and 3, and plug them back into the original unfactored expression, I will only get an even result when I use the number 2.
2 Case) 2^2+2=6 EVEN
3 Case) 3^2+2=11 ODD
Thanks