2020 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 9 Easy

A single bench section at a school event can hold either 7 adults or 11 children. When N bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of N?

  • A.

    9

  • B.

    18

  • C.

    27

  • D.

    36

  • E.

    77

Answer:B

Solution 1: The least common multiple of 7 and 11 is 77 . Therefore, there must be 77 adults and 77 children. The total number of benches \text { is } \frac{77}{7}+\frac{77}{11}=11+7=(\text{B}) 18

Solution 2: This is similar to Solution 1, with the same basic idea, but we don't need to calculate the LCM. Since both 7 and 11 are prime, their LCM must be their product. So the answer would be 7+11=(\text{B}) 18.

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