examday

/TMUA

Class $X$ contains $m$ students, and their mean mark in a test is $60$.

Class $Y$ contains $n$ students, and their mean mark in the same test is $70$.

The mean mark of all the students in the two classes combined is $64$.

Which of the following statements must be true?

• I $m>n$
• II $m$ is a multiple of $3$
• III If the mean mark of class $Y$ had been $74$ instead (with all class sizes and the class $X$ marks unchanged), the combined mean mark would have been $66$.