Practice Parity (Even/Odd) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The classification of integers as even (evenly divisible by 2, with no remainder) or odd (not divisible by 2).

Can you split it into two equal groups? Yes = even, no = odd.

Showing a random 20 of 50 problems.

Example 1

medium
If aa is even and bb is odd, what is the parity of aโ‹…ba \cdot b?

Example 2

easy
What is the parity of the product 6ร—96 \times 9?

Example 3

easy
What is the parity of 9+119 + 11?

Example 4

medium
Prove that n(n+1)n(n+1) is always even for any integer nn.

Example 5

easy
What is the parity of 3+83+8?

Example 6

hard
In a chessboard tour, a knight alternates between dark and light squares. After 77 moves, can the knight return to its starting square?

Example 7

easy
Is 2424 even or odd?

Example 8

easy
Without fully computing, determine the parity (odd or even) of 2,345+6,7822{,}345 + 6{,}782 and of 7ร—147 \times 14.

Example 9

easy
Is 4848 even or odd?

Example 10

medium
Without computing, find the parity of 123+456123+456.

Example 11

easy
Is 1,0001{,}000 even or odd?

Example 12

medium
If aa and bb are both odd, what is the parity of a+ba+b and of aร—ba\times b?

Example 13

medium
Two integers have an even sum. What can you say about their parities?

Example 14

easy
What is the parity of 3ร—73\times 7?

Example 15

easy
Classify each as odd or even without fully computing: (a) 100+201100 + 201, (b) 6ร—7ร—86 \times 7 \times 8, (c) 15215^2.

Example 16

challenge
Prove that the product of two odd numbers is always odd.

Example 17

medium
If nn is odd, what is the parity of n+1n+1? Of 2n2n?

Example 18

easy
Is the sum 5+6+75 + 6 + 7 odd or even?

Example 19

easy
What is the parity of 14โˆ’614 - 6?

Example 20

challenge
In a room, people shake hands; each handshake involves two people. Use parity to show the number of people who shook an odd number of hands is even.