Question

The average of 15 consecutive, positive whole numbers is equal to 55. What is the value of largest positive whole number?

1. 50.5
2. 65
3. 62
4. 72

Answer 1

Correct Answer - Option 3 : 62

Given:

Average of 15 consecutive whole numbers = 55

Concepts used:

Average = Sum of observations/Number of observations

Calculation:

Let first positive consecutive whole number be x.

⇒ Sum of 15 consecutive whole numbers = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8) + (x + 9) + (x + 10) + (x + 11) + (x + 12) + (x + 13) + (x + 14) ⇒ Sum of 15 consecutive whole numbers = 15x + 105

Average of 15 consecutive positive whole numbers = (15x + 105)/15

⇒ 55 = (15x + 105)/15

⇒ 55 × 15 = 15x + 105

⇒ 825 – 105 = 15x

⇒ 15x = 720

⇒ x = 720/15 = 48

⇒ Largest positive whole number = x + 14 = 48 + 14 = 62

∴ Largest positive whole number is 62.