Is the positive integer p even? (1) p^2 + p is even (2) 4p + 2 is even

Question

Is the positive integer p even?

(1) p^2 + p is even.
(2) 4p + 2 is even.

ArunSharma12 · Answer

statement 1:
even +even = even
odd + odd = even
p can be even or odd.

statement 2:
4p + 2 = even; 4p = even
p can be even or odd

combining both statements,
p still can be even or odd.
Ans: E

pranayeekarmakar · Answer

st 1. 
p(p+1)=even
so p may be even or odd as e.o=e or o.e=e
not sufficient

st2. 4p+2=even
4p always even so p can be even or odd not sufficient

st 1 + st2 no new information
so ans E

LeoN88 · Answer

I'll start with #2 because it's easy:

#2. 4p + 2 is even will always be even irrespective of any value of p, as it's  2*(2p+1) 
Any expression multiplied by 2 is even.

#1. p^2 + p is even for p=2 as well as p=3, so insufficient.

1+2 is also insufficient as both p=2 and p=3 satisfies both the stem together.

E

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