2016 AMC 8

Complete problem set with solutions and individual problem pages

Problem 11 Medium

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 132.

  • A.

    5

  • B.

    7

  • C.

    9

  • D.

    11

  • E.

    12

Answer:B

We can see that the original number can be written as 10a+b, where a represents the tens digit and b represents the units digit. When this number is added to the number obtained by reversing its digits, which is 10b+a, the sum would be 11a+11b. From this, we can construct the equation 11a+11b=132, which simplifies to a+b=12. Since there are 7 pairs of such digits a and b, (3,9), (4,8), (5,7), (6,6), (7,5), (8,4), (9,3), the answer would be \boxed{\textbf{(B) } 7}.

Related Problems
Problem 9 2016 AMC 8
Problem 10 2016 AMC 8
Problem 12 2016 AMC 8
Problem 13 2016 AMC 8
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