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28 Apr 2025, 07:57
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On a science exam, the scores received by a group of students represented a set of consecutive even integers. If the average of the scores was 35, what was the highest score received by a student?
(1) The difference between the highest and lowest scores received by the students was 22 points.
(2) The lowest score received by a student was 24.
(1) The difference between the highest and lowest scores received by the students was 22 points.
(2) The lowest score received by a student was 24.
05 Aug 2025, 09:01
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This is the method I feel is easier:
In a set of consecutive integers the average is always the middle term, which implies (when in ascending order) (First term F + Last term L)/2
Coming to the question:
Average = 35
=> (F + L)/2 = 35
=> F + L = 70. ------(1)
Option 1:
L - F = 22 ----(2)
From (1) and (2):
L = 46 (Sufficient)
Option 2:
F = 24
Substitute in (1) to get L = 46 (Sufficient)
Hence, EACH statement ALONE is sufficient.
In a set of consecutive integers the average is always the middle term, which implies (when in ascending order) (First term F + Last term L)/2
Coming to the question:
Average = 35
=> (F + L)/2 = 35
=> F + L = 70. ------(1)
Option 1:
L - F = 22 ----(2)
From (1) and (2):
L = 46 (Sufficient)
Option 2:
F = 24
Substitute in (1) to get L = 46 (Sufficient)
Hence, EACH statement ALONE is sufficient.
Bunuel
General Discussion
28 Apr 2025, 07:57
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Official Solution:
On a science exam, the scores received by a group of students represented a set of consecutive even integers. If the average of the scores was 35, what was the highest score received by a student?
First of all, in evenly spaced sets, such as a set of consecutive even integers, the average always equals the median. Next, the fact that the median of a set of consecutive even integers is 35, an odd integer, indicates that the number of scores (students) is even, with the median being the average of two middle scores. Thus, there would be an equal number of scores below and above the median. So we can have the following cases for the score distribution:
• {34, 36} - if there were two students;
• {32, 34, 36, 38} - if there were four students;
• {30, 32, 34, 36, 38, 40} - if there were six students;
and so on.
(1) The difference between the highest and lowest scores received by the students was 22 points.
There would be only one possible distribution with this difference between the highest and lowest scores, so we can determine the highest score received by a student (just for reference, it would be 46). Sufficient.
(2) The lowest score received by a student was 24.
Similarly, there would be only one possible distribution with this lowest score, so we can determine the highest score received by a student (again, it would be 46). Sufficient.
Answer: D
On a science exam, the scores received by a group of students represented a set of consecutive even integers. If the average of the scores was 35, what was the highest score received by a student?
First of all, in evenly spaced sets, such as a set of consecutive even integers, the average always equals the median. Next, the fact that the median of a set of consecutive even integers is 35, an odd integer, indicates that the number of scores (students) is even, with the median being the average of two middle scores. Thus, there would be an equal number of scores below and above the median. So we can have the following cases for the score distribution:
• {34, 36} - if there were two students;
• {32, 34, 36, 38} - if there were four students;
• {30, 32, 34, 36, 38, 40} - if there were six students;
and so on.
(1) The difference between the highest and lowest scores received by the students was 22 points.
There would be only one possible distribution with this difference between the highest and lowest scores, so we can determine the highest score received by a student (just for reference, it would be 46). Sufficient.
(2) The lowest score received by a student was 24.
Similarly, there would be only one possible distribution with this lowest score, so we can determine the highest score received by a student (again, it would be 46). Sufficient.
Answer: D
