AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 22 Medium

As shown in the diagram, if a, b, c are distinct nonzero digits, and the two-digit numbers \overline{ab} and \overline{bc}, formed in the counterclockwise direction, are both multiples of 7, then what is the sum of the largest and smallest possible three-digit numbers \overline{abc} that can be formed?

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  • A.

    991

  • B.

    1056

  • C.

    1126

  • D.

    1133

  • E.

    1198

Answer:C

Since the two-digit numbers \overline{ab} and \overline{bc} are both multiples of 7, they must be one of the following:   14, 21, 28, 35, 42, 49, 56, 63, 70, 84, 91, 98.

From these, the valid three-digit numbers \overline{abc} that can be formed are:   142, 214, 284, 356, 421, 428, 491, 498, 563, 635, 149, 842, 849, 914, 984.

The largest three-digit number is 984, and the smallest is 142. Their sum is:   984 + 142 = 1126.

The answer is \text{C}.

Related Problems
Problem 20 AMC 8 Daily Practice Round 9
Problem 21 AMC 8 Daily Practice Round 9
Problem 23 AMC 8 Daily Practice Round 9
Problem 24 AMC 8 Daily Practice Round 9
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