Five students wrote a quiz with a maximum score of 50 . The scores of four of the students were $42,43,46$, and 49 . The score of the fifth student was $N$. The average (mean) of the five students' scores was the same as the median of the five students' scores. The number of values of $N$ which are possible is
(A) 3
(B) 4
(C) 1
(D) 0
(E) 2
The five scores are $N, 42,43,46$, and 49 .

If $N46$, the median score is 46 .

If $N \geq 43$ and $N \leq 46$, then $N$ is the median.

We try each case.

If $N46$, then the median is 46 , so the mean should be 46 .

Since the mean is 46 , then the sum of the 5 scores must be $5 \times 46=230$.

Therefore, $N+42+43+46+49=230$ or $N+180=230$ or $N=50$, which is indeed greater than 46 .

We can check that the median and mean of $42,43,46,49$, and 50 are both 46 .

If $N \geq 43$ and $N \leq 46$, then the median is $N$, so the mean should be $N$.

Since the mean is $N$, then the sum of the 5 scores must be $5 N$.

Therefore, $N+42+43+46+49=5 N$ or $N+180=5 N$ or $4 N=180$, or $N=45$, which is indeed between 43 and 46 .

We can check that the median and mean of $42,43,45,46$ and 49 are both 45 .

Therefore, there are 3 possible values for $N$.

ANSWER: (A)