My answer is s and got to it by plugging numbers.

[deleted duplicate post]

Set up a table with three columns, and see which combinations of r and s result in an odd integer for rs+r :

r s rs+r
O O E (OxO+O = O+O = E)
O E O (OxE+O = E+O = O)
E O E (ExO+E = E+E = E)

We don't need to check r (E), s (E) combination, but if you want you can.

So rs+r would be odd only when r is odd and s is even. Plug this combination in the answer choices and see which one results in an even integer. Only the 2nd one (i.e. s) does.[/u]

imo b .. s

rs + r --> odd --> r(s+1) --> odd

say r = odd --> s+1 --> odd --> s - even

r(s+1) --> odd

say r = even --> s+ 1 --> odd --> not possible...

both r and s+1 have to be odd for the expression to be odd....

if s+ 1 is odd then we have s as even