Question

If p is a positive integer, which could be an odd integer?

(A) 2p + 2
(B) p^3 - p
(C) p^2 + p
(D) p^2 - p
(E) 7p - 3

Answer 1

`p>0\\\\(A)\ \ \ 2p+2=2(p+1)\ \rightarrow\ \ even\ number\\\\(B)\ \ \ p^3-p=p(p^2-1)=p(p-1)(p+1)\ \rightarrow\ \ even\ number\\\\(C)\ \ \ p^2+p=p(p+1)\ \rightarrow\ \ even\ number\\\\(D)\ \ \ p^2-p=p(p-1)\ \rightarrow\ \ even\ number\\\\(E)\ \ \ 7p-3=6p-4+p+1=2(3p-2)+p+1\\\\p-odd\ \rightarrow\ \ (p+1)- even\ \rightarrow\ (7p-3)-even\ number\\\\p-even\ \rightarrow\ \ (p+1)- odd\ \rightarrow\ (7p-3)-odd\ number\\\\Ans.\ E`

Answer 2

`p > 0 \Rightarrow`


`2p+2` (even)


`p^3-p` (odd or even)


`p^2 + p` (even)


`p^2 - p` (even)


`7p - 3` (ODD); 7p odd, 7p-3 = (odd)-(odd)=(odd)