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jmc

number theory junior

Problem

The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?
(A)
(B)
(C)
(D)
Solution
Let be the number of boys and be the number of girls. For and to be integers, must cancel out with the denominator, and the smallest possible value is . This yields boys. The minimum number of students is .
Final answer
B