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06 Feb 2024, 02:30
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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:
35%
(medium)
Question Stats:
78% (02:05) correct
22%
(02:18)
wrong
based on 144
sessions
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Among 100 students in a class, 57 like football and 68 like basketball. The maximum possible number of students who like both football and basketball is represented by 'a', and the minimum possible number of students who like both football and basketball is represented by 'b'. What is the value of 'a' minus 'b'?
A. 12
B. 19
C. 23
D. 28
E. 32
A. 12
B. 19
C. 23
D. 28
E. 32
Among 100 students in a class, 57 like football and 68 like basketball. The maximum possible number of students who like both football and basketball is a and the minimum possible number of students who like both football and basketball is b. What is the value of a-b?
06 Feb 2024, 03:32
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The overlap is minimum when Neither = 0 and it is maximum when one set lies inside the other set.
Here is a video discussing this with the help of diagrams: Max Min in Overlapping Sets
When Neither = 0,
Total = F + B - Both
100 = 57 + 68 - Both
Both = 25 (minimum value)
Maximum value of Both = 57
Difference = 57 - 25 = 32
Answer (E)
Here is a video discussing this with the help of diagrams: Max Min in Overlapping Sets
When Neither = 0,
Total = F + B - Both
100 = 57 + 68 - Both
Both = 25 (minimum value)
Maximum value of Both = 57
Difference = 57 - 25 = 32
Answer (E)
Bunuel
06 Feb 2024, 08:25
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Maximum possible number of students who like both = 57
total number of students who like both ,57 + 68 = 125
57+68-b=100 , b=57+68-100=25
A-B
=57-25
=32
IMO-E
total number of students who like both ,57 + 68 = 125
57+68-b=100 , b=57+68-100=25
A-B
=57-25
=32
IMO-E
