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

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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

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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.