BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:16 am
There are 2 groups of students who took a history test. 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?
(1) Of the students who took the test, 10 were in Group A and 12 were in Group B.
(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.
Answer:
E
Source: Official guide
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
