Two decks of cards are there. Each deck contains 20 cards, with numbers from 1 to 20 written on them. A card is drawn of random from each deck, getting the numbers x and y what is the probability that log x + log y is a positive integer. Logs are taken to the base 10.

log x + log y = log(xy)

log xy is integer when (x,y) = (1, 10), (10, 1), (10, 10), (5, 20), (20, 5), (2, 5), (5, 2)

The required probability = 7 / 400

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