Average of five two-digit consecutive even natural

Solution

Five even numbers: a, (a + 2) , (a + 4) , (a + 6) , (a + 8) Five odd numbers: b, (b + 2) , (b + 4) , (b + 6) , (b + 8) Given, (a + 6) + (b + 2) = 59 Or, a + b = 51 ------ (I) b + 8 = a + 2 - 3 Or, a – b = 9 --------- (II) On adding equation I and II, We get, a + b + a – b = 51 + 9 Or, 2a = 60 Or, 'a' = 30 On putting value of 'a' in equation II, We get, 'b' = 30 - 9 = 21 So, the five even numbers: 30, 32, 34, 36, 38

And the five odd numbers: 21, 23, 25, 27, 29

Statement I:

Required difference = 36 - 21 = 15

So, statement I is true.

Statement II:

Third odd number = 25, which is a perfect square.

So, statement II is true.

Statement III:

First even number = 30, and 30 > 27.

So, statement III is true.

Therefore, all three statements I, II and III are true.