Math, asked by gulshankumar3896, 5 months ago

Which of the following is always even
options

(a) Sum of three odd numbers

(b) Sum of two odd numbers

(c) Sum of one even and one odd numbers

(d) none of these ​

Answers

Answered by Anonymous
1

The sum of two odd numbers is always even.

  • Odd numbers are those numbers which can not be divided by two. For example - 3, 7, 17 , 21 etc.
  • Thus, the sum of two odd numbers will always be even.
  • For example- 3 + 5 = 8 or 11 + 17 = 28
  • Whereas, if two or more odd numbers  are multiplied, there product is always odd and also the sum of an even number of odd numbers is even.
Answered by amitnrw
0

Given :  Few statement about odd even numbers

To Find :     Which of the following is always even   options

(a) Sum of three odd numbers

(b) Sum of two odd numbers

(c) Sum of one even and one odd numbers

(d) none of these ​

Solution:

Even number = 2k

Odd number = 2k + 1  

where k belongs to integer

a) Sum of three odd numbers

2a + 1 + 2b + 1 + 2c + 1

= 2(a + b + c) + 3

= 2(a + b + c) + 2 + 1

= 2(a + b + c + 1) + 1

= 2k + 1

= odd

(b) Sum of two odd numbers

= 2a + 1 + 2b + 1

= 2a + 2b + 2

= 2(a + b + 1)

= 2k

= EVEN

(c) Sum of one even and one odd numbers

= 2a  + 2b + 1

= 2(a + b) + 1

= 2k + 1

= odd

Sum of two odd numbers is always EVEN

Learn More:

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