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There are three sets A, B, and C, which contain a total of 13 unique integers. A total of n prime numbers is distributed among them. Set A has four numbers. The smallest and largest numbers in set A are 2 and 6. Set B has five numbers, but only two of them are prime numbers (the others are composite). Set C has four numbers. The product of the smallest and largest numbers in set C is 23, which is the highest number in all three sets. If n < 8, and the total number of prime numbers in set A is greater than that in set B, then which set has the least number of prime numbers?

1. B
2. C
3. Can be B and C
4. Can't be determined

Correct answer: Can't be determined

Solution

Set B is known to have exactly two prime numbers, while set A has more primes than set B. However, the prime count in set C is not fixed by the given data. Since n < 8 only limits the total number of primes, it still allows multiple valid distributions, so the set with the least primes cannot be uniquely identified.

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