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06 Aug 2024, 19:15
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
54% (03:36) correct
46%
(03:41)
wrong
based on 63
sessions
History
Date
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. 24
B. 23
C. 22
D. 21
E. 20
A. 24
B. 23
C. 22
D. 21
E. 20
Bunuel
We need total to be \(38 * 5= 190\)
To give Amit least lets give others maximum keeping the constraints in mind.
Max to least : \(50, \hspace{2mm} 49,\hspace{2mm} 48,\hspace{2mm} 32,\hspace{2mm} 11 \)
Amit's least marks \(=11\)
To give Amit max lets lets give others as less as possible keeping the constraints in mind.
Least to max = \(31,\hspace{2mm} 32,\hspace{2mm} 40,\hspace{2mm} 42,\hspace{2mm} 45\) or \(31, \hspace{2mm}32, \hspace{2mm}41,\hspace{2mm} 42, \hspace{2mm}44 \) etc.
Amit's max marks : \(=31\)
Thus max - least \(= 31 -11 = 20\)
Ans E
Hope it helped.
11 Aug 2024, 00:41
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stne
How did you decide to go with 40,42 45 or 41,42 and 44?
