SAT Math — SAT Question of the Day

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SAT Math — SAT Question of the Day

QOD2015_1029
Explanation
On some questions, we can count possibilities or confirm a specific possibility by listing out the details. On this question, since the answer choices involve a large total number of balls, listing is not too practical. There must be an easier way to solve the question! We can look for a pattern that we can use to determine the answer without listing.

We know that balls go into the sack in the order (G)(B)(R)(Bk)(W). There are 5 colors involved. If we put in 5 balls, we'd end with a white ball. But, we ended with a black ball. That would happen if we put in only 4 balls, or 4 on the next time around after a set of 5, which would be 9 balls. We could count and see that the next black is the 14th ball.

We can see some patterns in those numbers. Each instance of a black ball is separated by 5, and is an instance that ends with a 4 or a 9: 4, 9, 14, 19... Or, each instance of a black ball is one less than a multiple of 5. Either fact gives us enough information to answer the question. The only answer choice fitting the pattern is (C), with a final digit of 4. In this case, the colors will be cycled through 18 times (since 18×5=90), and then we don't quite get through the 19th cycle--we stop on the fourth ball in that cycle, the black one.

The correct answer is (C).

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