2011 AMC 12A Problem 2

Attempt Problem 2 of the 2011 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 12A solutions, or check the answer key.

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2.

There are 55 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

(C,A,E,D,B)(C, A, E, D, B)

(C,A,D,E,B)(C, A, D, E, B)

(C,D,E,A,B)(C, D, E, A, B)

(C,E,A,D,B)(C, E, A, D, B)

(C,E,D,A,B)(C, E, D, A, B)

Answer: E
Concepts:logical deduction
Difficulty rating: 840
Solution:

Coin CC is drawn as a complete, unbroken circle, so nothing covers it and it lies on top.

Reading the remaining overlaps, each coin's uncovered arc shows it sits above the next: CC covers E,E, EE covers D,D, DD covers B,B, and AA covers BB while lying under the others. This gives the top-to-bottom order (C,E,D,A,B).(C, E, D, A, B).

Thus, the correct answer is E.

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