GMAT Club Official Solution:At a training center, 4 interns and 6 mentors took the same certification test. What was the average (arithmetic mean) score of all 10 test-takers?The question asks for the average score of all 10 test-takers.
(1) The total score of the mentors was 180 points, and the average score of the interns was 5 points less than the average score of the mentors.
Since there were 6 mentors, the mentors’ average score was:
180/6 = 30
The interns’ average score was 5 points less, so:
30 - 5 = 25
Since there were 4 interns, their total score was:
4 * 25 = 100
So the total score of all 10 test-takers was:
180 + 100 = 280
Therefore, the average score was:
280/10 = 28
Sufficient.
Alternatively, after finding the two group averages, we can reason as follows:The ratio of the number of interns to the number of mentors is:
4:6 = 2:3
So the overall average is between 25 and 30, and its distances from the two group averages are in the reverse ratio:
3:2
The difference between the two group averages is:
30 - 25 = 5
So the 5-point gap is split into 3 parts and 2 parts. Each part is 1 point.
Thus, the overall average is:
25 + 3 = 28
(2) If one of the interns had scored 20 points more, the total score of the group would have increased by 20.
Since there were 10 test-takers, the group average would have increased by:
20/10 = 2
The new average would have been 30, so the actual average was:
30 - 2 = 28
Sufficient.
Each statement alone is sufficient.
Answer: D.