11+ Maths Solved Topic Wise Questions

1. Odd Numbers

Odd numbers are numbers that cannot be arranged in pairs i.e., all integers except the multiples of 2 are odd numbers. If we divide an odd number by 2, then it will leave a remainder. For example: 11, 13, 29, 55, etc. Odd numbers are just the opposite concept of even numbers.

1.1 How to know if the number is odd or even?

Any integer that cannot be completely divided by 2, and leaves a remainder is called an odd number.

Let’s see some examples and check if the number is odd or not.

1. 25 – if we divide 25 by 2 i.e. 25 ÷ 2 then remainder comes out as 1, so 25 is an odd number.
2. 17 – check this by the same method. You will find 17 ÷ 2 gives remainder 1. So, 17 is not an even number. It is an odd number.
3. 8 – if we divide the given number 8 by 2 i.e. 8 ÷ 2 then the remainder is 0. So, 8 is an even number.
4. 18 – again if we divide the given number 18 by 2 i.e. 18 ÷ 2 then the remainder is 0. So, 18 is an even number.

But what if you are given very large numbers, say, 35647 and 954238? How to check if the given number is odd or even without dividing it by 2?

That particular number in one’s place will tell whether the number is odd or even.

• Odd Numbers end with 1, 3, 5, 7, 9
• Even numbers end with 0, 2, 4, 6, 8

For example, 35647 has 7 in one's place - So, 85647 is an odd number. 954238 has 8 in one’s place - So, 954238 is an even number.

Hence, summarising the concept of odd numbers as follows:

1.2 List of odd numbers from 1 to 100

1.3 Properties of Odd Numbers

Following are the properties of odd numbers including operations with even numbers:

Addition Property:

• The sum of an even number and odd number is an odd number. For example, 8 + 5 = 13
• The sum of two odd numbers is an even number. For example, 5 + 11 = 16

Subtraction Property:

• The difference between an even number and an odd number gives an odd number. For example, 12 – 7 = 5
• The difference between two odd numbers gives an even number. For example, 13 – 9 = 4

Multiplication Property:

• The multiplication of an even number and an odd number gives an even number. For example, 8 x 5 = 40
• The multiplication of two odd numbers gives an odd number. For example, 7 x 9 = 63

Division Property:

If the two numbers do not divide exactly, i.e. the quotient will be a decimal value and not a whole number, hence, will neither be even nor odd. However, when the two numbers divide exactly, we refer to the following properties:

• An even number divided by an odd number is even. For example, 20h ÷ 5 = 4
• An odd number divided by an odd number will always be odd. For example, 63 ÷ 7 = 9