Question

The average of three consecutive odd numbers is 14 more than one third of the first of these numbers .what is the last of these numbers 1)17 2)19 3)15 4)data inadequate

Answer 1

We have 3 consecutive odd numbers

So they are in AP with d = 2

So, let the numbers be a - 2, a, a + 2

Average = (a - 2 + a + a + 2) / 3

= 3a /3 = a

So, we are given

Avg = 1/3 of first number + 14

So, a = 1/3 [ a - 2 ] + 14

a = a/3 - 2/3 + 14

2/3 a = 14 - 2/3

2/3 a = 42/3 - 2/3

2/3 a = 40/3

a = 20

So numbers are: 20 - 2, 20, 20 + 2

They are: 18, 20, 22

As the numbers are even numbers, answer is option D i.e. data inadequate

Answer 2

Let the 3 consecutive odd numbers be x-2, x, x+2

Also,       Average = 3x/3 = x
=> x = 14 + (x-2)/3 => 3x = 42 + x - 2 => 2x = 40=> x = 20
So, the numbers are Even but the required numbers should be odd
Thus the D option is correct