Explanation

In this question, the colors of the cards are not truly essential. The point is that each card is worth 2, 3, 5, 7, or 13 points. Since those are all primes, and we have the product of a series of draws, we can determine exactly how many draws of each time occurred by finding the prime factorization of 5,733,000:



Since is divisible by 9, the number 5733 is divisible by 9.







We have identified the 10 cards that were drawn. We need the number of black 7 cards, which correspond to the factors of 7. There are two, so we now know the correct answer is (D).

Another straightforward way to solve this question is to divide 5,733,000 by 7, obtaining 819,000, then to divide 819,000 by 7, obtaining 117,000, and then attempting to divide by 7 a third time and finding it doesn't go in evenly, meaning that 5,733,000 has two factors of 7.

Note that this question would be somewhat more complicated if we didn't know the number of cards that were drawn. For example, in such a case, we wouldn't know whether the factors were generated by two black 7 cards and a black 9 card, or by 63 black 7 cards!

The correct answer is (D).