There are 2 groups of students who took a history test. Was the averag

Target question: Was the average (arithmetic mean) score of the students in Group A higher than the average score of the students in Group B who took the test?

Statement 1: Of the students who took the test, 10 were in Group A and 12 were in Group B.
To calculate the average score for each group, we need:
- The sum of all scores in each group
- The number of students in each group

Statement 1 provides the number of students in each group, but we still don't know the sum of scores for each group.
Statement 1 is NOT SUFFICIENT

Statement 2: On the test, the highest score achieved was achieved by a Group B student and the lowest score achieved was achieved by a Group A student.
This just tells us about 1 student from each group.
Also, we still need to know the number of students in each group.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine both statements, we know the total number of students in each group, and we know a TINY BIT about 1 score from each group.
As such, the combined statements are NOT SUFFICIENT

If you're not 100% convinced, consider the following scenarios that satisfy BOTH statements:
Case a: The Group A scores are {1,1,1,1,1,1,1,1,1,1} and the Group B scores are {5,5,5,5,5,5,5,5,5,5,5,5,}. In this case, the answer to the target question is NO, Group A's average score is NOT greater than Group B's average score
Case b: The Group A scores are {1,99,99,99,99,99,99,99,99,99} and the Group B scores are {2,2,2,2,2,2,2,2,2,2,2,10}. In this case, the answer to the target question is YES, Group A's average score IS greater than Group B's average score
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Solution:

Let there be x students in Group A and y students in Group B.

Let sum of scores in Group A = a and that of Group B =b.

Hence the average of Group A = a/x and the average of Group B = b/x.

We are asked if average of Group A> average of Group B

or if a/x > b/x ?

St (1):- Of the students who took the test, 10 were in Group A and 12 were in Group B.

Given x=10,y=12 but we are not aware of the values of a and b. (Insufficient)

St(2):- On the test, the highest score achieved was achieved by a Group B student and the lowest score achieved was achieved by a Group A student.

No specific information regarding the value of a, b, x, y is provided. (Insufficient)

On combining both, we still do not have the specific values of a, b, x, y. (Insufficient)

Thus option (e)

Hope this helps

Devmitra Sen (GMAT Quant Expert)

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