Picking numbers is the best strategy here

(1) says cd+c=even . This is possible when c is even and is possible even when c is odd.INSUFFICINET
Example if c=2 and d=2 then cd+c=4+2=6

if c=3 and d=1 then cd+c=3+1=4

(2) says that (c+2)(d+2)=even. Again this condition can be satisfied if c is even as well as when c is odd.INSUFFICIENT

Example if c=2 and d=2 then (2+2)(2+2)=16

if c=5 and d= 2 then (5+2)(2+4)=42

Combining both the statements we get,


Example if c=2 and d=5 then cd+c=10+2=12 and (c+2)(d+2)=(2+2)(5+4)=36

if c=3 and d=4 then cd+c+12+3=15 but (c+2)(d+4)=40

Why do I think the answer is E.Am I missing something??

Even i thought that the answer was E. But apparently, its C Any help?

here is what I did

Take 2 set of numbers c = 1 and d = 2, c = 1 and d = 1
Both the sets use a off value for c, the value of d is changed to have one even and one odd.

Solve both the equations. You will find that with the first set statement is odd but the second is even. With the second set the first is even but second is odd. So with a odd value of c it is not possible to meet both the conditions. So c will have to be even.

Does this make sense?