We have nine digits $2,3,3,7,7,0,1,9,4$...... | Free GMAT Practice Question | GMAT Panda

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We have nine digits 2, 3, 3, 7, 7, 0, 1, 9, 4, each used exactly once to form three three-digit integers. What is the greatest possible sum of these three integers?

Explanation	Calculations	Help
$We express the total sum of the three three-digit numbers by summing their place-value contributions.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We maximize the sum by assigning the three largest digits to the hundreds places, the next three largest to the tens places, and the remaining to the units places.$	$h_{1} + h_{2} + h_{3} = 9 + 7 + 7 t_{1} + t_{2} + t_{3} = 4 + 3 + 3 u_{1} + u_{2} + u_{3} = 2 + 1 + 0$
$We substitute these values into the expression for the total sum and find its value.$	$S = 100 \times 23 + 10 \times 10 + 3 S = 2300 + 100 + 3 S = 2403$

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C

We have nine digits 2, 3, 3, 7, 7, 0, 1, 9, 4, each used exactly once to form three three-digit integers. What is the greatest possible sum of these three integers?

Explanation	Calculations	Help
$We express the total sum of the three three-digit numbers by summing their place-value contributions.$	$S = 100 \times (h_{1} + h_{2} + h_{3}) + 10 \times (t_{1} + t_{2} + t_{3}) + (u_{1} + u_{2} + u_{3})$	Theory & Tactics Method Card ALG6-A Click to view full details
$We maximize the sum by assigning the three largest digits to the hundreds places, the next three largest to the tens places, and the remaining to the units places.$	$h_{1} + h_{2} + h_{3} = 9 + 7 + 7 t_{1} + t_{2} + t_{3} = 4 + 3 + 3 u_{1} + u_{2} + u_{3} = 2 + 1 + 0$
$We substitute these values into the expression for the total sum and find its value.$	$S = 100 \times 23 + 10 \times 10 + 3 S = 2300 + 100 + 3 S = 2403$

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C