Question

The average of squares of four positive consecutive odd numbers is 149. Find the sum of 3 times the smallest number and 4 times the largest number?
1. 81
2. 76
3. 87
4. 98

Answer 1

Correct Answer - Option 3 : 87

Given:

Average of square of 4 consecutive odd numbers = 149

Formula used:

Average of 'n' numbers = (Sum of 'n' numbers)/n

Calculation:

Let, the first odd number = a

∴ Next three odd numbers = (a + 2), (a + 4) and (a + 6)

Sum of square of 4 consecutive odd numbers = 149 × 4

= 596

∵ a² + (a + 2)² + (a + 4)² + (a + 6)² = 596

⇒ a2 + a2 + 4a + 4 + a2 + 8a + 16 + a2 + 12a + 36 = 596

⇒ 4a2 + 24a + 56 = 596

⇒ 4a2 + 24a + 56 - 596 = 0

⇒ a2 + 6a - 135 = 0

⇒ a2 + 15a - 9a - 135 = 0

⇒ a(a + 15) - 9(a + 15) = 0

⇒ (a - 9)(a + 15) = 0

∴ a - 9 = 0

⇒ a = 9

a + 15 = 0

⇒ a = (-15)

∵ Negative value cannot be taken as the numbers are positive.

∴ a = 9

∴ Smallest number = 9

Largest number = 15

∴ Sum of 3 times smallest and 4 times largest = (3 × 9) + (4 × 15)

= 27 + 60

= 87