Question

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 $N?$

$9$

$18$

$27$

$36$

$77$

Answer: B

Concepts:least common multiple divisibility

Difficulty rating: 1070

Video solution:

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Written solution:

If the equal number of adults and children is $P$ , then the adults use $P/7$ bench sections and the children use $P/11$ bench sections. Thus $N=P\left(\dfrac17+\dfrac1{11}\right)=\dfrac{18P}{77}$ .

The least positive integer occurs when $P=77$ , giving $N=18$ . Thus, B is the correct answer.

2020 AMC 10A Problem 9

Answer: B

Difficulty rating: 1070

Video solution:

Written solution:

Problem 9 in Other Years