A positive integer $n$ is a multiple of 7 . The square root of $n$ is between 17 and 18 . How many possible values of $n$ are there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Since the square root of $n$ is between 17 and 18 , then $n$ is between $17^{2}=289$ and $18^{2}=324$.

Since $n$ is a multiple of 7 , we need to count the number of multiples of 7 between 289 and 324 . Since $41 \times 7=287$ and $42 \times 7=294$, then 294 is the smallest multiple of 7 larger than 289 . Since $46 \times 7=322$ and $47 \times 7=329$, then 322 is the largest multiple of 7 smaller than 324 . This means that the multiples of 7 between 289 and 324 are $42 \times 7=294,43 \times 7=301$, $44 \times 7=308,45 \times 7=315$, and $46 \times 7=322$, of which there are 5 .

(We note that we could have determined that there were 5 such multiples by calculating $46-42+1$ which equals 5 .)

Therefore, there are 5 possible values for $n$.

ANSWER: (D)