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

Question

In a class of 21, how many scored above the class average (arithmetic mean) on the final exam?

(1) The class average is 78.
(2) The class median is 78.

JeffTargetTestPrep · Accepted Answer

n = 21, and we need to answer the question:

# of above-average scores = ?

Statement One Alone:

=> The class average is 78.

If every score was 78, then 0 score was above average.

Whereas, if 10 scores were 77, 1 score was 78, and 10 scores were 79, then 10 scores were above average.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> The class median is 78.

Notice that, in each of the two cases that we used for testing above, the median is equal to 78. So, we can use those cases here as well.

Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Notice that we can use the same cases as above for testing.

The two statements together are not sufficient.

Answer: E

KarishmaB · Answer

The class has 21 students so the median will be the 11th score. (1) The class average is 78. Anything is possible. All 21 could have scored exactly 78 so no one scored above average. or 20 people could have scored 77 and 1 could have scored 98 so 1 scored above average etc. Not sufficient. (2) The class median is 78. The 11th person scored 78. We don't know what the average is so not sufficient. Using both together also, we cannot say how many scored more than 78. Many cases are posisble. For example, All 21 could have scored exactly 78 (No one scored above average) or The scores could have been 68, 69, ... 78, 79, ... 88 (10 people scored above average) etc. Answer (E) Check out this question on mean, median and range: https://anaprep.com/sets-statistics-mea ... -question/

gmatophobia · Answer

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

mmdfl · Answer

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)

Steven_Iallonardo · Answer

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

Danny134 · Answer

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.

karansinghania · Answer

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

Bunuel · Answer

______________________________________
Yes.

Juangui17 · Answer

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.

Aalto700 · Answer

I made a careless mistake,  above

jmaxr · Answer

I approached this in the following manner by testing cases.

1. if average = 78 and everyone scored a 78 then nobody scored above the average. 
if average = 78 and nobody scored a 78 then we could have outliers that heavily impact the average. Such as a few students scoring 0s or 100s, which gives us no definitive way to determine a number above the average. 
 NOT SUFFICUENT

2. if Median= 78 that tells us nothing about the average. we could have ...0,0, 78 ,79,79... or ...78,78, 78, 78,78... 
 NOT SUFFICUENT

Together: if Average= 78 and Median= 78 then we are stuck with these two possibilities ...77,77, 78 ,79,79 where we have 10 scores above the average or ...78,78, 78 ,78,78... where we have no scores above the average. 
 NOT SUFFICUENT

Answer Choice E

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards