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What is the ratio of the variance of the first n positive multiples of 5 to the variance of the first n positive multiples of 10?

1. 1: 2
2. 1: 1
3. 1: 4
4. 1: 5

Correct answer: 1: 4

Solution

Multiples of 5 are 5 times {1,...,n} so their variance is 25*Var({1,...,n}); multiples of 10 are 10 times {1,...,n} so their variance is 100*Var({1,...,n}). The ratio is 25:100 = 1:4.

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