Data Sufficiency

VJesus12 wrote:If m and n are integers, then what is the value of (-1)^m + (-1)^n + (-1)^m · (-1)^n ?

(1) m = 23522101
(2) n = 63522251

The OA is the option D.

Is each statement sufficient? I thought the answer should be C.

Experts, I would appreciate your help here. Please.

We have to get the value of (-1)^m + (-1)^n + (-1)^m · (-1)^n.

Case 1: If m = n = 0, then (-1)^m + (-1)^n + (-1)^m · (-1)^n = (-1)^0 + (-1)^0 + (-1)^0 · (-1)^0 = 1 + 1 + 1*1 = 1 + 1 + 1 = 3.
Case 2: If m and n are even, then (-1)^e + (-1)^e + (-1)^e · (-1)^e = 1 + 1 + 1*1 = 1 + 1 + 1 = 3.
Case 3: If m and n are odd, then (-1)^o + (-1)^o + (-1)^o · (-1)^o = -1 - 1 + -1*-1 = -1 - 1 + 1 = -1.
Case 4: If one between m and n is even and the other is odd, then (-1)^e + (-1)^o + (-1)^e · (-1)^o = 1 - 1 + 1*-1 = 1 - 1 - 1 = -1.
Case 5: If one between m and n is even and the other is 0, then (-1)^e + (-1)^0 + (-1)^e · (-1)^0 = 1 + 1 + 1*1 = 1 + 1 + 1 = 3.
Case 6: If one between m and n is odd and the other is 0, then (-1)^o + (-1)^0 + (-1)^o · (-1)^0 = -1 + 1 - 1*1 = -1 + 1 - 1 = -1.

Let's see each statement one by one.

(1) m = 23522101

=> m is Odd. We do not know whether n is 0/even/odd. Case 3/4/6 are applicable; for each case, the resultant value is -1. Sufficient.

(2) n = 63522251

=> n is Odd. It is the same statement as Statement 1, thus, sufficient.

The correct answer: D

Hope this helps!

-Jay
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