1985 AHSME Problem 29
1985 AHSME Problems/Problem 29 Problem In their base $10$ representations, the integer $a$ consists of a sequence of $1985$ eights and the integer $b$ consists of a sequence of $1985$ fives. What is the sum of the digits of the base $10$ representation of the integer $9ab$? $\mathrm{(A)\ } 15880 \qquad \mathrm{(B) \ }17856 \qquad \mathrm{(C) \ } 17865 \qquad \mathrm{(D) \ } 17874 \qquad \mathrm{(E) \ }19851$ Solution Factor: $a = 888\dots 888 = 8\underbrace{(111\dots 111)}{1985 \times \text{1’s}}$ $b = 555\dots 555 = 5\underbrace{(111\dots 111)}{1985 \times \text{1’s}}$...