Question

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\dfrac{1}{3}$ of all the ninth graders are paired with $\dfrac{2}{5}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

$\dfrac{2}{15}$

$\dfrac{4}{11}$

$\dfrac{11}{30}$

$\dfrac{3}{8}$

$\dfrac{11}{15}$

Answer: B

Concepts:ratio and proportion fraction

Difficulty rating: 1300

Video solution:

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Written solution:

Let there be $s$ sixth graders and $n$ ninth graders. The number of paired ninth graders equals the number of paired sixth graders, so $\dfrac13 n=\dfrac25 s.$

This gives $5n=6s$ , so $n:s=6:5$ . The total number of students is therefore proportional to $11$ parts.

The paired ninth graders make up $\dfrac13\cdot\dfrac6{11}=\dfrac2{11}$ of all students, and the paired sixth graders make up $\dfrac25\cdot\dfrac5{11}=\dfrac2{11}$ of all students. Altogether, $\dfrac4{11}$ of the students have a buddy.

Thus, B is the correct answer.

2015 AMC 8 Problem 16

Answer: B

Difficulty rating: 1300

Video solution:

Written solution:

Problem 16 in Other Years