In a class of 21, how many scored above the class average (arithmetic

Number of students in the class = 21

Statement 1

(1) The class average is 78.

The statement alone is not sufficient as we don't have any information on the distribution of marks among the students. If all the students have scored 78 on the test, no student will have scored above the class average (arithmetic mean) on the final exam, however, the marks can be distributed in such a way that the positive difference (w.r.t the class mean) of some students compensates for the negative difference (w.r.t the class mean) of some other students. Hence, without additional information, the exact number of students cannot be found.

We can eliminate options A and D.

Statement 2

(2) The class median is 78

The statement alone is not sufficient as we don't have any information on the distribution of marks among the students. If all the students have scored 78 on the test, the class average will be 78. However, no student will have scored above the class average (arithmetic mean) on the final exam. On the contrary, the marks can be distributed in such a way that the positive difference (w.r.t the class mean) of some students compensates for the negative difference (w.r.t the class mean) of some other students. Hence, without additional information, the exact number of students cannot be found.

We can eliminate option B.

Combined

The statements combined do not help either because we still don't have any information on the individual scores or any information that can help find the number of students who scored above the class average (arithmetic mean) on the final exam.

Option E

Lets call g_i each grade of the student i, with g_1<=g_2<=...<=g_21
1) Knowing only the average a set is not enough to know how many elements of the series are bigger than the avg. INSUFF
2) We don't know the average, even we knowing the median. INSUFF
1&2) g_11=78. This is tricky, because we can think that g_12,g_13,...,g_21 are bigger than 78 (so, 10 numbers would be bigger than 78), but they can all be equal to 78 (g1=g2=...=g21 => 0 grades bigger than avg) or can be in many other configurations ( g2=g3=...=g20=78, g1=77, g21=79 => 1 grade bigger than avg; etc ). INSUFF
E)

­1) Insuff alone
2) Insuff alone
Combined: It could be 10 below average and/or median and then the other values could be equal to the median and the average/or above average.
For example:
77,77,77,77,77,77,77,77,77,77,78,78,78,78,78...
or 77,77,77,77,77,77,77,77,77,77,78,78,78,79...
or 77,77,77,77,77,77,77,77,77,77,78,79,79,79... and so on so forth. 
It is not possible to identify clearly how many people scored above average -> E

­Since A and B alone are clearly insufficient, on combining them both we can get numerous case like:

1. all 10 students on the right side of median scored above 78.
2. any 1 student scored above 78 and the remaining scored equal to 78.

As such, there can be multiple scenarios, and in the absence of more information we will not be able to reach to a definite answer. Hence, Combing 1 and 2 is also insufficient. The correct answer is E.

­What would be the case if the question had specified that all scores are distinct? The answer would be C right?

______________________________________­
Yes.

I guess this helps....

If the statement said and the mode is 78 then we could say we have a evenly distributed bell curve, hence we can now how many are above the mean, media and mode which is in the middle of the curve for the 21 students so Its 10.

But since we only have median and mean, it could be skewed.

I made a careless mistake, above