Some sevenths of my card collection is 66 cards. Some elevenths of my card collection is 63 cards. Which of these can be the number of cards in my card collection?

Let total cards be n. From 'some sevenths' (meaning k/7 for some integer k), we have kn/7 = 66, so n = 462/k. Similarly, from 'some elevenths', n = 693/j for integers j, k. This means n must be a common divisor of 462 and 693. GCD(462, 693) = 231. Checking divisors: 231 works (7 × 33 = 231, 11 × 21 = 231, and both give remainders). Other options don't satisfy both conditions.