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26 May 2026, 19:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
62% (02:35) correct
38%
(02:29)
wrong
based on 105
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At a music audition, judges assigned scores to 9 applicants. Among the applicants, 3 tied for the lowest score of 14 points, and 2 tied for the highest score of 65 points. If the median score of the 9 applicants was 50 points, what was the average (arithmetic mean) score of the 9 applicants?
(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.
(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.
(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
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M47-172
04 Jun 2026, 01:00
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GMAT Club Official Solution:
At a music audition, judges assigned scores to 9 applicants. Among the applicants, 3 tied for the lowest score of 14 points, and 2 tied for the highest score of 65 points. If the median score of the 9 applicants was 50 points, what was the average (arithmetic mean) score of the 9 applicants?
Since exactly 3 applicants scored the lowest score of 14, exactly 2 applicants scored the highest score of 65, and the median score was 50, the scores, arranged in ascending order, can be written as:
14, 14, 14, a, 50, b, c, 65, 65
The question asks for the average score, so we need the value of a + b + c.
(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.
After removing the three 14s and the two 65s, the remaining scores are:
a, 50, b, c
The median of these 4 scores is 56, so:
(50 + b)/2 = 56
50 + b = 112
b = 62
But a and c are still not fixed.
Not sufficient.
(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
After removing the three 14s and the two 65s, the remaining scores are:
a, 50, b, c
The range is 12, so:
c - a = 12
But this does not determine a + b + c.
Not sufficient.
(1)+(2) From statement (1):
b = 62
So the remaining scores are:
a, 50, 62, c
From statement (2) the range of these numbers, c - a, is 12.
Since the difference between 50 and 62 is already 12, and a <= 50 < 62 <= c, we must have:
a = 50 and c = 62
Thus, the 9 scores are:
14, 14, 14, 50, 50, 62, 62, 65, 65
The average can be found.
Sufficient.
Answer: C.
At a music audition, judges assigned scores to 9 applicants. Among the applicants, 3 tied for the lowest score of 14 points, and 2 tied for the highest score of 65 points. If the median score of the 9 applicants was 50 points, what was the average (arithmetic mean) score of the 9 applicants?
Since exactly 3 applicants scored the lowest score of 14, exactly 2 applicants scored the highest score of 65, and the median score was 50, the scores, arranged in ascending order, can be written as:
14, 14, 14, a, 50, b, c, 65, 65
The question asks for the average score, so we need the value of a + b + c.
(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.
After removing the three 14s and the two 65s, the remaining scores are:
a, 50, b, c
The median of these 4 scores is 56, so:
(50 + b)/2 = 56
50 + b = 112
b = 62
But a and c are still not fixed.
Not sufficient.
(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
After removing the three 14s and the two 65s, the remaining scores are:
a, 50, b, c
The range is 12, so:
c - a = 12
But this does not determine a + b + c.
Not sufficient.
(1)+(2) From statement (1):
b = 62
So the remaining scores are:
a, 50, 62, c
From statement (2) the range of these numbers, c - a, is 12.
Since the difference between 50 and 62 is already 12, and a <= 50 < 62 <= c, we must have:
a = 50 and c = 62
Thus, the 9 scores are:
14, 14, 14, 50, 50, 62, 62, 65, 65
The average can be found.
Sufficient.
Answer: C.
General Discussion
28 May 2026, 02:41
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Answer should be C
we have given the numbers in following sequence 65,65, a, b, 50, c, 14, 14,14
1) From this we can find (b+50)/2 = 56 so b= 62. still a and c are unknowns. so not sufficient
2) From this we can see a-c= 12. still not sufficient
But if we combine both, we have only sequence of a=62, b=62, 50, c=50 to satisfy both conditions so both together sufficient.
we have given the numbers in following sequence 65,65, a, b, 50, c, 14, 14,14
1) From this we can find (b+50)/2 = 56 so b= 62. still a and c are unknowns. so not sufficient
2) From this we can see a-c= 12. still not sufficient
But if we combine both, we have only sequence of a=62, b=62, 50, c=50 to satisfy both conditions so both together sufficient.
29 May 2026, 00:37
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Arranging the scores in order:
14, 14, 14, a, 50, c, d, 65, 65
Since the median of all 9 applicants is 50, the 5th score is 50.
Analyzing Statement (1)
If the scores of 14 and 65 are removed, the remaining scores are:
a, 50, c, d
The median of these 4 numbers is 56, so:
(50+c)/2=56 so c=62
We still do not know a or d, so the average cannot be determined.
Statement (1) is insufficient.
Analyzing Statement (2)
The range of the remaining scores is 12.
This only tells us the difference between the highest and lowest remaining scores. Multiple sets of values are still possible, so the average cannot be determined.
Statement (2) is insufficient.
Combining Statements (1) and (2)
From statement (1), we know c=62.
Using the range of 12, different possibilities still exist, such as:
So the average score still cannot be uniquely determined.
Correct Answer: E
14, 14, 14, a, 50, c, d, 65, 65
Since the median of all 9 applicants is 50, the 5th score is 50.
Analyzing Statement (1)
If the scores of 14 and 65 are removed, the remaining scores are:
a, 50, c, d
The median of these 4 numbers is 56, so:
(50+c)/2=56 so c=62
We still do not know a or d, so the average cannot be determined.
Statement (1) is insufficient.
Analyzing Statement (2)
The range of the remaining scores is 12.
This only tells us the difference between the highest and lowest remaining scores. Multiple sets of values are still possible, so the average cannot be determined.
Statement (2) is insufficient.
Combining Statements (1) and (2)
From statement (1), we know c=62.
Using the range of 12, different possibilities still exist, such as:
- 50,50,62,62
- 50,51,62,62
So the average score still cannot be uniquely determined.
Correct Answer: E
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