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Question

A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying X + Y ≤ 5. What is the number of possible pairs of values of (X, Y)?

This question was previously asked in
CDS I 2018 Elementary Mathematics Previous Year Paper (04-Feb-2018)
The correct answer is

7

Divisibility by three requires X + Y + 10 to be a multiple of three. With X ≥ 1 and X + Y ≤ 5, the sum X+Y is 2 or 5. There are 2 and 5 pairs respectively, totalling 7.

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