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Bunuel
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­Five students, including Amit, appear for an examination in which 06 Aug 2024, 19:15
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85% (hard)

Question Stats:

55% (03:36) correct 45% (03:39) wrong based on 62 sessions

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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. 24
B. 23
C. 22
D. 21
E. 20­
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stne
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­Five students, including Amit, appear for an examination in which Updated on: 13 Aug 2024, 22:35
Originally posted by stne on 10 Aug 2024, 12:15.
Last edited by stne on 13 Aug 2024, 22:35, edited 1 time in total.
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Bunuel
­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
Show more
­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.­
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harshchougule
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­Five students, including Amit, appear for an examination in which 11 Aug 2024, 00:41
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stne

Bunuel
­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
­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 D

Hope it helped.­
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­How did you decide to go with 40,42 45 or 41,42 and 44?
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stne
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­Five students, including Amit, appear for an examination in which 11 Aug 2024, 01:21
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harshchougule

stne

Bunuel
­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
­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 D

Hope it helped.­
­How did you decide to go with 40,42 45 or 41,42 and 44?
Show more
­Hi

Total should be \(190\) and after subtracting Amit's and his closest friend we should get \(127\)

The last three numbers do not matter as long as they add upto \(127\). So you could also have \(40,43,44\)

Main thing is Amit's marks cannot be more than \(31,\) and then we adjust the mark's of others keeping the constraints in mind.

Hope it is clear now?­
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