Question

How many students scored more than the average marks of the class in a test?
I. The average marks of the class was 70.
II. 10 students scored above the arithmetic mean of the class.

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

In problems related to averages and percentages, be sure to differentiate between the total and the group-specific conditions, such as those above or below the mean.

Answer 1

The Correct Option is B

Let the total number of students in the class be \( n \). - From condition I, the average marks of the class were 70. This means the total marks of the class, denoted by \( T \), is: \[ T = 70 \times n \] - From condition II, 10 students scored above the arithmetic mean (average) of the class. This means there are 10 students whose scores are greater than 70.
Since the total number of students who scored above the average is 10, and no other information is provided, we can conclude that the number of students who scored more than the average is 10.
Thus, the correct answer is \( \boxed{2} \).