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06 Aug 2026, 03:57
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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?
(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.
(2) If one of the interns had scored 20 points more, the average score of all 10 test-takers would have been 30.
(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.
(2) If one of the interns had scored 20 points more, the average score of all 10 test-takers would have been 30.
06 Aug 2026, 03:57
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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:
\(\frac{180}{6} = 30\)
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:
\(\frac{280}{10} = 28\)
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:
\(\frac{20}{10} = 2\)
The new average would have been 30, so the actual average was:
\(30 - 2 = 28\)
Sufficient.
Each statement alone is sufficient.
Answer: D
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:
\(\frac{180}{6} = 30\)
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:
\(\frac{280}{10} = 28\)
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:
\(\frac{20}{10} = 2\)
The new average would have been 30, so the actual average was:
\(30 - 2 = 28\)
Sufficient.
Each statement alone is sufficient.
Answer: D
