Question 1017905: If 3(m+n) is even, then which of the following is also even?
a. m+n
b. m
c. n
d. 3n+1
Answer by reviewermath(1029)   (Show Source):
You can put this solution on YOUR website! If 3(m+n) is even, then which of the following is also even?
a. m+n
b. m
c. n
d. 3n+1
Solution:
One way of solving this problem is by substituting values to the variables.
Select values for m and n such that 3(m+n) is an even number.
Case 1: Both m and n are odd numbers.
Suppose m = 1 and n = 5, then 3(1+5) = 18 is an even number.
a) m + n = 1 + 5 = 6 (even)
b) m = 1 (odd)
c) n = 5 (odd)
d) 3n + 1 = 3(5) + 1 = 16 (even)
So b and c are eliminated from the given choices.
Case 2: Both m and n are even numbers.
Suppose m = 2 and n = 4, then 3(2+4) = 18 is an even number
a) m + n = 2 + 4 = 6 (even)
d) 3n + 1 = 3(4) + 1 = 13 (odd).
Therefore, the final answer is letter "a".
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