Three classes in a school all took the same test. Class 1 achieved a mean score of 61, Class 2 achieved a mean score of 63, and Class 3 achieved a mean score of 70. The mean score of the students for all three classes combined was 65. Class 1 contains twice as many students as Class 2. Which one of the following statements about the number of students in Class 3 is true?

Answer:

Class 1 contains twice as many students as Class 2, so if there are 𝑛 students in Class 2, then there
are 2𝑛 students in Class 1.
The total of all of the scores in Class 1 must be 61 × 2𝑛 = 122𝑛.
The total of all of the scores in Class 2 must be 63𝑛.
If there are 𝑚 students in Class 3, then the total of all the scores in Class 3 must be 70𝑚.
The total score of all of the students must be 65 × (2𝑛 + 𝑛 + 𝑚),
so 195𝑛 + 65𝑚 = 122𝑛 + 63𝑛 + 70𝑚.
This simplifies to 10𝑛 = 5𝑚, so 𝑚 = 2𝑛.
The number of students in Class 3 is 2𝑛, which is the same as the number of students in Class 1.
The answer is D