1979 AHSME Problems/Problem 5

Problem 5

Find the sum of the digits of the largest even three digit number (in base ten representation) which is not changed when its units and hundreds digits are interchanged.

$\textbf{(A) }22\qquad \textbf{(B) }23\qquad \textbf{(C) }24\qquad \textbf{(D) }25\qquad \textbf{(E) }26$

Solution

Solution by e_power_pi_times_i

Since the number doesn't change when the units and hundreds digits are switched, the number must be of the form $aba$. We want to create the largest even $3$-digit number, so $a = 8$ and $b = 9$. The sum of the digits is $8+9+8 = \boxed{\textbf{(D) } 25}$.

See also

1979 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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