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The variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16. Find m + n.

1. 10
2. 12
3. 14
4. 18

Correct answer: 18

Solution

Variance of first n naturals = (n² - 1)/12 = 10 => n² = 121 => n = 11. Variance of first m even naturals {2,4,...,2m}: mean = m+1, variance = (m²-1)/3 = 16 => m² = 49 => m = 7. So m + n = 18.

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