Each of the nine digits $1,2,2,3,4,6,7,7,$ and $9$... | Free GMAT Practice Question | GMAT Panda

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Each of the nine digits 1, 2, 2, 3, 4, 6, 7, 7, and 9 is used once to form three three-digit integers. What is the greatest possible sum of the three integers?

Explanation	Calculations	Help
$We write the total sum of the three integers in terms of their hundreds, tens, and units digits using place values.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We assign the largest digits to the hundreds places, the next largest to the tens places, and the smallest to the units places to maximize the sum.$	$h_{1} + h_{2} + h_{3} = 9 + 7 + 7 t_{1} + t_{2} + t_{3} = 6 + 4 + 3 u_{1} + u_{2} + u_{3} = 2 + 2 + 1$
$We substitute these totals into the expression for S and then find its value.$	$S = 100 \times 23 + 10 \times 13 + 5 S = 2300 + 130 + 5 S = 2435$

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A

Each of the nine digits 1, 2, 2, 3, 4, 6, 7, 7, and 9 is used once to form three three-digit integers. What is the greatest possible sum of the three integers?

Explanation	Calculations	Help
$We write the total sum of the three integers in terms of their hundreds, tens, and units digits using place values.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We assign the largest digits to the hundreds places, the next largest to the tens places, and the smallest to the units places to maximize the sum.$	$h_{1} + h_{2} + h_{3} = 9 + 7 + 7 t_{1} + t_{2} + t_{3} = 6 + 4 + 3 u_{1} + u_{2} + u_{3} = 2 + 2 + 1$
$We substitute these totals into the expression for S and then find its value.$	$S = 100 \times 23 + 10 \times 13 + 5 S = 2300 + 130 + 5 S = 2435$

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A