SOLUTION: N.M and T are integers N+M is an odd number M+T is an odd number Which of the following must be true: a) NxT is even b) NxT is odd c) N+T is odd d) N+T is even e) N-T i

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Question 390606: N.M and T are integers
N+M is an odd number
M+T is an odd number
Which of the following must be true:
a) NxT is even
b) NxT is odd
c) N+T is odd
d) N+T is even
e) N-T is odd
Found 2 solutions by Edwin McCravy, scott8148:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
N+M is an odd number
M+T is an odd number 

Case 1:  If M is even, N and T are both odd 
         (in order to make both their sums with M odd).

Case 2:  If M is odd, N and T are both even 
         (in order to make both their sums with M even).

So N and T are the same type (parity) of integer, i.e., both odd or both even.

  a) NxT is even
This is false in case 1, since an odd times an odd is an odd

b) NxT is odd
This is false in case 2, since an even times an even is an even

c) N+T is odd
This is false in both cases, since if you add two odds or two evens, you get an even.

d) N+T is even
This is true in both cases, since if you add two odds or two evens, you get an even.

e) N-T is odd
This is false in both cases, since if you subtract two odds or two evens, you get an even.

So the only correct statement is d)

Edwin

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
(N+M) + (M+T) is even ___ two odd numbers add to an even number

rearranging ___ N+T+2M is still even

2M is even ___ divisible by 2

N+T is even ___ an even number subtracted from an even number leaves an even number