SAT Math Multiple Choice Practice Question 131: Answer and Explanation

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Question: 131

21. In a deck of 12 cards, each card has one of the symbols below on each side. Some cards have the same symbols on both sides; some cards have different symbols. If every symbol appears on at least two different cards, and Symbols A and B together appear on a total of 13 sides, what is the maximum number of cards that could have Symbol D on both sides?

A. One
B. Two
C. Three
D. Four
E. Five

Correct Answer: D


D. The 12 cards have a total of 24 sides, and symbols A and B represent 13 of them. Because you want C to show up as much as possible, the easiest way to do so is to have only As and Bs on 6 cards (12 sides), with one more on a side of another card. Now you can put a C on the other side of that card and another C on some other card. You've taken care of the rule that each symbol must appear on at least two cards, and you've used a total of 8 cards. Thus, you're left with a maximum of 4 cards that could be all Ds.

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