1992 AMC 8 Problem 15

Attempt Problem 15 of the 1992 AMC 8 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 1992 AMC 8 solutions, or check the answer key.

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15.

What is the 19921992nd letter in this sequence?

ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC\cdots

A

B

C

D

E

Answer: C
Concepts:modular arithmeticpattern recognition

Difficulty rating: 910

Solution:

The sequence is the 99-letter block ABCDEDCBAABCDEDCBA repeated again and again.

Since 1992=9×221+3,1992 = 9 \times 221 + 3, the 19921992nd letter is the 33rd letter of a block, which is C.C.

Thus, the correct answer is C .

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