The average of eight consecutive odd numbers is 48. Find the sum of the fifth and seventh numbers.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 3)

Answer 1

Given:

The average of eight consecutive odd numbers is 48.

Concept used:

Average = Sum of elements/Number of elements

Calculation:

Let the eight consecutive odd number be x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10), (x + 12), (x + 14)

Average of eight consecutive odd numbers = 48

⇒ {x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14)}/8 = 48

⇒ (8x + 56) = 384

⇒ 8x = 328

⇒ x = 41

So, 5th number = 41 + 8 = 49

7th number = 41 + 12 = 53

Total = 49 + 53

⇒ 102

∴ The required answer is 102.

Shortcut Trick

The average of eight consecutive odd numbers is 48,

This means the position of "48" is in the middle 4.5th, among the 8 consecutive odd numbers.

So, the numbers are 1^st = 41, 2^nd = 43, 3^rd = 45, 4^th = 47, (48) , 5^th = 49, 6^th = 51, 7^th = 53, 8^th = 55

The sum of 5th and 7th number (49 + 53) = 102