Q66. A Question is given followed by two Statements I and
II. Consider the Questions and the Statements. Question : If the average marks in a class are 60, them what is the number of students in the class? Statement-I : The highest marks in the class are 70 and the lowest marks are 50. Statement-II : Exclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

We need to find the number of students (N) in the class, given that the average marks are 60. **Statement I: The highest marks in the class are 70 and the lowest marks are 50.** This statement provides the range of marks but gives no information about the number of students.

Thus, Statement I alone is insufficient. **Statement II: Exclusion of highest and lowest marks from the class does not change the average.** Let S be the sum of marks of N students.

So, S/N = 60 => S = 60N. Let H be the highest marks and L be the lowest marks. After excluding them, the new sum is S - H - L, and the new number of students is N - 2. The statement says the new average is still 60: (S - H - L) / (N - 2) = 60.

Substitute S = 60N: (60N - H - L) / (N - 2) = 60. 60N - H - L = 60(N - 2) 60N - H - L = 60N - 120 -H - L = -120 => H + L = 120. This statement alone tells us that the sum of the highest and lowest marks is 120.

It does not provide the number of students (N). Thus, Statement II alone is insufficient. **Combining Statement I and Statement II:** From Statement I, H = 70 and L = 50. Their sum is H + L = 70 + 50 = 120.

This value (120) is consistent with the condition derived from Statement II (H + L = 120). However, this consistency does not introduce any new information that allows us to determine N.

The equation H + L = 120 does not contain N, so N cannot be found. Therefore, even both statements together are insufficient. This question tests data sufficiency and understanding of averages.