Each of the nine digits $0,2,3,3,5,6,7,9,9$...... | Free GMAT Practice Question | GMAT Panda

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Each of the nine digits 0, 2, 3, 3, 5, 6, 7, 9, 9 is used once to form 3 three-digit integers. What is the greatest possible sum of the 3 integers?

Explanation	Calculations	Help
$We express the sum of the three three-digit integers in terms of their hundreds, tens, and units digits using place values.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We maximize the total by placing the largest digits in the hundreds positions, the next largest digits in the tens positions, and the smallest digits in the units positions.$	$h_{1} + h_{2} + h_{3} = 9 + 9 + 7 t_{1} + t_{2} + t_{3} = 6 + 5 + 3 u_{1} + u_{2} + u_{3} = 3 + 2 + 0$
$We substitute these sums into the expression for S and calculate.$	$S = 100 \times 25 + 10 \times 14 + 5 = 2500 + 140 + 5 = 2645$

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A

Each of the nine digits 0, 2, 3, 3, 5, 6, 7, 9, 9 is used once to form 3 three-digit integers. What is the greatest possible sum of the 3 integers?

Explanation	Calculations	Help
$We express the sum of the three three-digit integers in terms of their hundreds, tens, and units digits using place values.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We maximize the total by placing the largest digits in the hundreds positions, the next largest digits in the tens positions, and the smallest digits in the units positions.$	$h_{1} + h_{2} + h_{3} = 9 + 9 + 7 t_{1} + t_{2} + t_{3} = 6 + 5 + 3 u_{1} + u_{2} + u_{3} = 3 + 2 + 0$
$We substitute these sums into the expression for S and calculate.$	$S = 100 \times 25 + 10 \times 14 + 5 = 2500 + 140 + 5 = 2645$

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A