Question

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?

$76531$

$86724$

$87431$

$96240$

$97403$

Video solution:

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Written solution:

To construct two five digit numbers, first digits of the numbers from the left must be as great as possible. Therefore, the leftmost unused number must be either of the greatest two numbers. This means the first digit must be either of $9,8,$ the second digit must be either of $7,6,$ the third digit must be either of $5,4,$ the fourth digit must be either of $3,2$ and the last digit must be either of $1,0.$

The only one of the given numbers that satisfy this is $87431.$

Thus, the answer is C .

2012 AMC 8 Problem 16

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Written solution:

Problem 16 in Other Years