On a given day, 50 students in a certain class took a math test. Some

Question

On a given day, 50 students in a certain class took a math test. Some of the students took the test on test paper A, and the remaining of the 50 students took the test on test paper B. What is the average score on the test for the 50 students?

(1) The average score for the students who take the test A was 75.
(2) The average score for the students who take the test В was 77.

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kb26 · Answer

average scores for each of the groups are given in each statements. but, we are not given any group size. so, both are not sufficient. Ans, E.

dhart · Answer

E , The numbr of student in in any class is unknown from combining both the statements

dhart · Answer

stated as above in the post

Kevi · Answer

On a given day, 50 students in a certain class took a math test. Some of the students took the test on test paper A, and the remaining of the 50 students took the test on test paper B. What is the average score on the test for the 50 students?

(1) The average score for the students who take the test A was 75. 
No info about test B
Insufficient

(2) The average score for the students who take the test В was 77.
No info about test A

(1)&(2) 
No clear info about the number of students who took either test. 
Insufficient

E

counterclash1 · Answer

Correct Answer : E

The information in the two statements even when combined is not giving any information regarding weighted average of the distribution of the students as the distribution can be anything (1,49), (49,1), etc. leading to difference in the overall average.

BrunoDGPrep · Answer

Before looking at the statements, I’d ask: what do we actually need to find the average for all 50 students? Well... We need two things: we need is the sum of their scores and the number of students, but we already know the number of students (50), right?
The total sum of the scores is the sum of group A’s scores and the sum of group B’s scores. So we have:
Total average = (sum of group A’s scores + sum of group B’s scores) / 50

Notice that we don’t need to know each student’s individual score. If we can determine the combined total, that is enough.

If x is the number of students who took paper A. Then the remaining (50 - x) students took paper B. We don't need to add new variables.

Statement (1) 
The average for group A is 75, so the sum of that group’s scores is 75x. Remember:
Sum = Average × Number of students
But we don’t know the sum of group B’s scores. Even if we knew x, that missing information would prevent us from finding the total average. So, we can say that Statement (1) alone is insufficient.

Statement (2) 
The average for group B is 77, so the sum of that group’s scores is 77(50 - x).
This time, we don’t know the sum of group A’s scores. Statement (2) alone is also insufficient.

Now... Let's take  Statements (1) and (2) together 
Now we can express both groups’ totals:

Total average =   / 50, which is...
 = (75x + (77)(50) - 77x) / 50, which is...
 = ((77)(50) - 2x) / 50 
 = 77 - x/25

Have we determined the average? Not yet. We have an expression for it, but its value still depends on x, the number of students who took paper A. Neither statement tells us that number.

Simply put, I cannot get a value. Therefore, even together, the statements are insufficient. The answer is E.

I hope it's clear.

On a given day, 50 students in a certain class took a math test. Some

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On a given day, 50 students in a certain class took a math test. Some