Question

What is the average of all the two digit even numbers?

Answer 1

Answer:

7.9

Step-by-step explanation:

First let's find the total number of 2 digit even number:

For a number to be even the units place should have any one of these five digits (0,2,4,6,8) and in the teens place we can have any digit. Thus for two digit even number with 1 we have give possibilities (10,12,14,16,18) similarly for numbers with 2 too numbers with 9 in teens place. So we're have a total of 40 two digit even number.

Now making a series in Arithmetic Progression:

10,12,14,....,96,98

We need to find the sum of this series

Here, n being total number of teens we have 40

The first number, a is 10

Common different, d is 2

Therefore sum of this series = n/2[2a + (n-1)d]

= 40/2[2(40) + (40-1)2]

= 20[80 + 78]

= 316

Now for the average of this series = 316/40 = 7.9