Odd or Even? Trivia Quiz

Answer: Parity

In layman's term, we often say a number is either odd or even. However, in the field of mathematics, this is referred as the parity of a number.

Answer: Natural numbers

Natural numbers (1, 2, 3...) are also known as counting numbers. Meanwhile, a rational number is a number which can be written in the form of p/q, where both p and q are integers (..., -2, -1, 0, 1, 2...) and q is not equal to 0.

On the other hand, irrational numbers are numbers that are not rational numbers. Natural numbers, rational numbers and irrational numbers are subsets for real numbers.

Answer: 1

Let us take a look at the first few binary numbers and their corresponding values in base 10.

0: 0
1: 1
10: 2
11: 3
100: 4
101: 5
110: 6
111: 7

Here, we notice that if a binary number ends with 1, then it is odd. If it ends with 0, then it is even.

Answer: All prime numbers are odd.

All prime numbers are odd, except 2. The number 2 is the only even prime number.

Yes, 0 is an even number, since it is divisible by 2 without any remainder.

We can prove that the sum of any 2 odd numbers is an even number. Let a and b be 2 odd numbers. Then we can write a = 2m + 1 and b = 2n + 1., where m and n are integers. So, a + b = (2m + 1) + (2n + 1) = 2(m+n) + 2 = 2(m+ n + 1). We now let m + n + 1 = h, and we see that the sum is in the form of 2h. So, the sum is an even number.

Answer: 0! and 1!

Note that both 0! and 1! equal 1. 2! = 2 x 1 = 2. All the remaining factorial operations (2!, 3!, 4!...) will result in even numbers.

Answer: 123456789 x 987654321

In order for us to find out the answer, we can just carry out the operations for the last digit.

The product of 2 odd numbers is also an odd number itself. But if one or both of the numbers is even, then the product will be an even number.

Meanwhile, the sum of 2 odd numbers or 2 even numbers is even. But the sum of an odd number and an even number is odd.

Answer: f(x) = cos x

Since f(x) = cos x is an even function, we can write cox x = cos (-x). The function f(x) = sin x is an odd function, where sin x = -sin (-x), or in general, f(x) = -f(-x).

Answer: 180

An example of an odd function is f(x) = sin x.

Answer: V

In Roman numerals, I is 1, V is 5, X is 10, L is 50, C is 100, D is 500.

Answer: A < B

The sum of all the numbers from 1 to 100 = 1 + 3 + 5 +...+ 97 + 99 = (99 + 1)(50)/2 = 2500. We evaluate this by multiplying the sum of the first term and the last term by the total number of terms, and then we divide it by 2 (since each number will be calculated twice, otherwise). While the sum of all the numbers from 1 to 100 = 2 + 4 + 6 +...+ 98 + 100 = 2550.

Another way to solve this problem is by noticing that 2 is greater than 1, 4 is greater than 3, and so on. So eventually we will get A less than B.

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Mr. Odd and Mr. Even would like to thank you for your help in solving these problems. They are now good friends again after finding out that there are equally many odd and even numbers for the set of positive integer.

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I hope you enjoy my quiz and learn something new as well. Thanks for playing and have a nice day!