1979 AHSME Problems/Problem 5

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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 (Problems • Answer Key • Resources) Preceded byProblem 4 Followed byProblem 6 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 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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