Set S contains all the integers from 10 to 99. $S_1$ , a subset of S, contains all the numbers of S, in which both the digits are even. $S_2$ , also a subset of S, contains all the numbers of S, in which both the digits are odd. What is the ratio of sum of all elements in $S_1$ to sum of all elements in $S_2$ ?

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\frac{108}{275}

\frac{216}{275}

Correct

\frac{2}{3}

\frac{275}{216}

\frac{3}{2}

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Official Explanation

Official

Even numbers: 20, 22, 24, 26, 28; 40, 42, 44, 46, 48; 60, 62, 64, 66, 68; 80, 82, 84, 86, 88.

The mean of each group is 24, 44, 64, 84.

The mean of the entire set is (44 + 64) / 2 = 54.

Therefore, the sum of the set is 54 × 4 × 5 = 1080 (4 = number of groups; 5 = number of terms in each group).…

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What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.