GMAT Word Problems: What is the greatest possible sum…

Each of the nine digits 0, 1, 1, 4, 5, 6, 8, 8, and 9 is used once to form 3 three-digit integers. What is the greatest possible sum of the 3 integers?

word problemsordersums of digits

Explanation	Calculations	Help
$We express the sum of the three 3-digit integers in terms of their hundreds, tens, and units digits using place values.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$
$We maximize the total by placing the largest digits in the highest-weight positions (hundreds), the next largest in the tens, and the smallest in the units.$	$h_{1} + h_{2} + h_{3} = 9 + 8 + 8 t_{1} + t_{2} + t_{3} = 6 + 5 + 4 u_{1} + u_{2} + u_{3} = 1 + 1 + 0$
$We substitute these sums into the expression for S and calculate.$	$S = 100 \times 25 + 10 \times 15 + 2 = 2500 + 150 + 2 = 2652$

2,652 (C)

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