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, $\boxed{\text{(C)}\ \text{C}}$ .

1992 AJHSME (Problems • Answer Key • Resources)
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

Page

Toolbox

Search

1992 AJHSME Problems/Problem 15

Problem

Solution

See Also