1. When the following are evaluated, how many of the answers are odd numbers?
$$
1^{2}, 2^{3}, 3^{4}, 4^{5}, 5^{6}
$$

A 1
B 2
C 3
D 4
E 5
Solution
C
When two odd numbers are multiplied, the result is another odd number. Therefore an odd integer raised to a positive power results in an odd number. Likewise, an even integer raised to a positive power results in an even number.
It follows that, of the given numbers, $1^{2}, 3^{4}$ and $5^{6}$ are odd numbers, while $2^{3}$ and $4^{5}$ are even.
Therefore 3 of the given expressions evaluate to an odd number.