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08 Jul 2025, 10:20
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Seven students took a quiz and each got a different score between 0 and 100. The average score was 30, so the total of all scores is 7 × 30 = 210. The median score, which is the fourth highest when the scores are arranged in order, was 27.
To make the highest score as small as possible, we want the other six scores to be as high as possible without breaking the rules. The three scores below the median must be less than 27 and different from each other. The largest possible ones are 26, 25, and 24. The three scores below the median are now 24, 25, and 26, and the median is 27.
That leaves three more scores: two above the median and one highest score. To keep the highest score low, we can choose the next two numbers to be just below it, like the highest score minus 2 and minus 1. So the top three scores are: M-2, M-1, and M.
Now, we add all the scores:
24 + 25 + 26 + 27 + (M-2) + (M-1) + M.
This adds up to 75 + 27 + (M-2 + M-1 + M) = 75 + 27 + (3M - 3) = 99 + 3M.
We know the total must be 210, so:
99 + 3M = 210 => 3M = 111 => M = 37.
So, the smallest possible highest score is 37.
To make the highest score as small as possible, we want the other six scores to be as high as possible without breaking the rules. The three scores below the median must be less than 27 and different from each other. The largest possible ones are 26, 25, and 24. The three scores below the median are now 24, 25, and 26, and the median is 27.
That leaves three more scores: two above the median and one highest score. To keep the highest score low, we can choose the next two numbers to be just below it, like the highest score minus 2 and minus 1. So the top three scores are: M-2, M-1, and M.
Now, we add all the scores:
24 + 25 + 26 + 27 + (M-2) + (M-1) + M.
This adds up to 75 + 27 + (M-2 + M-1 + M) = 75 + 27 + (3M - 3) = 99 + 3M.
We know the total must be 210, so:
99 + 3M = 210 => 3M = 111 => M = 37.
So, the smallest possible highest score is 37.
Bunuel
08 Jul 2025, 10:23
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correct answer is (D)
Average score= 30
30= sum of all scores/7
sum of scores = 210
Median = 27
Since all students received different scores, assume the 3 lowest scores to be 24, 25, and 26, and the 3 highest scores to be x, x+1, and x+2.
210=24+25+26+27+x+x+1+2
x=35
The MINIMUM possible HIGHEST SCORE will be x+2=37 (D)
Average score= 30
30= sum of all scores/7
sum of scores = 210
Median = 27
Since all students received different scores, assume the 3 lowest scores to be 24, 25, and 26, and the 3 highest scores to be x, x+1, and x+2.
210=24+25+26+27+x+x+1+2
x=35
The MINIMUM possible HIGHEST SCORE will be x+2=37 (D)
Bunuel
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08 Jul 2025, 10:24
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Solution :
We know that there are seven students in the class, and each received a different integer score between 0 and 100.
We are also told the mean is 30 and the median is 27.
So, the sum would be 210. And, also in order to minimize the possible value, we have to maximize the other values. So, the possible values could be 24,25,26,27,36,37,x = 210. If we could get minimum highest value by keeping the other values after median as 36 & 37. So, our best possible answer for the minimum possible value for the highest score is 35.
Answer: 35
We know that there are seven students in the class, and each received a different integer score between 0 and 100.
We are also told the mean is 30 and the median is 27.
So, the sum would be 210. And, also in order to minimize the possible value, we have to maximize the other values. So, the possible values could be 24,25,26,27,36,37,x = 210. If we could get minimum highest value by keeping the other values after median as 36 & 37. So, our best possible answer for the minimum possible value for the highest score is 35.
Answer: 35
Bunuel A class of seven students took a quiz, and each received a different integer score between 0 and 100. If the average (arithmetic mean) score was 30 and the median was 27, what is the minimum possible value for the highest score?
