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02 Dec 2022, 21:11
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
75% (04:35) correct
25%
(05:03)
wrong
based on 4
sessions
History
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Time
Result
Not Attempted Yet
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
A) 20
B) 22
C) 24
D) 21
E) 23
Source: CAT 2022
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03 Dec 2022, 00:38
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Noida
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
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