Answer: C

Let $n$ be the number of new students. The total of all scores is $24(78) + 90n = 1{,}872 + 90n$. It must also equal $81(24 + n) = 1{,}944 + 81n$. So $1{,}872 + 90n = 1{,}944 + 81n$, which gives $9n = 72$ and $n = 8$.

Choice B divides the needed $72$ points by $90 - 78 = 12$, but each new student is only $90 - 81 = 9$ points above the new mean.

Why the other choices are wrong

• A. 3 is the increase in the mean score, not the number of new students.
• B. This divides 72 by 90 - 78 = 12. Each new student scores only 9 points above the new mean of 81, so divide by 9.
• D. 9 is the difference between 90 and the new mean, 81. The 72 points the original students fall short must be divided by 9.