4. The teacher has just returned the corrected assignments in a class. The average of all the grades received is 6; the average grade of the assignments that scored at least 6 is 7, while the average of the others is 4. What portion of the class scored less than 6?
(A) $1 / 4$
(B) $1 / 3$
(C) $2 / 5$
(D) $3 / 8$
(E) $2 / 7$
Problem 4. The correct answer is (B).

Suppose there are $a$ people who have scored at least 6 and $b$ people who have scored less than 6. The sum of all sufficient scores is thus $7a$ and the sum of insufficient scores is equal to $4b$. The fact that the overall average is equal to 6 is equivalent to having $7a + 4b = 6(a + b)$, which simplifies to $a = 2b$. The number of people who scored less than 6 is therefore half the number of those who scored at least 6, meaning that the former are $1/3$ of the total.