1992 AJHSME Problems/Problem 15

Problem

What is the $1992^\text{nd}$ letter in this sequence?

\[\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots\]

$\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}$

Solution

The sequence consists of repeated strings of 9 letters, $\text{ABCDEDCBA}$. When 1992 is divided by 9, the remainder is 3, and so the 1992nd letter in the sequence is the 3rd letter of the smaller string, $\boxed{\text{(C)}\ \text{C}}$.

See Also

1992 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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