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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
A) 20 B) 22 C) 24 D) 21 E) 23
Source: CAT 2022
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Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
A) 20 B) 22 C) 24 D) 21 E) 23
Source: CAT 2022
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Let the marks of the students when arranged in ascending order is represented as \(M_1\), \(M_2\), \(M_3\), \(M_4\) and \(M_5\)
We know that no two students got the same and marks and exactly three students got more than 32.
As Amit scored the least his score is \(M_1\)
Minimum value of \(M_1\)
To minimize \(M_1\), we have to maximize the other scores. \(M_3, M_4, M_5 \)can take 48, 49 and 50 respectively. \(M_2\) can take 32. We can find the distance from the mean for each of the scores and obtain the value of \(M_1\).
\(M_1\) = 11
Maximum value of \(M_1\)
To get the maximum value of \(M_1\), the numbers must be as close as possible to the mean. \(M_4\) can be 33 and \(M_2\) can be 32. As \(M_2\) is six less than the mean, \(M_1\) can be seven below mean.
Therefore \(M_1\) = 38 - 7 = 31
Difference = 31 - 11 = 20
Option A
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.