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This is an old Venn Diagram question and I've read through some previous posts about how to solve it but some problems prop up.
Original Question:
In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?
I wonder: the question asks for those that "pass either subject" not those that "fail either subject." So then doesn't 47% represent those that have failed either but not both?
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Hi there,
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Failed in A = 35
Failed in B = 42
Failed in both = 15
Failed in only A but not in other = 35-15 = 20 (i.e Passed in B but failed in A)
Failed in only B but not in other = 42-15 = 27 (i.e Passed in A but failed in B)
Total that failed in either but not in both (i.e Passed in one but failed in other) = 20 + 27 = 47
Failed in A = 35 Failed in B = 42 Failed in both = 15 Failed in only A but not in other = 35-15 = 20 (i.e Passed in B but failed in A) Failed in only B but not in other = 42-15 = 27 (i.e Passed in A but failed in B)
Total that failed in either but not in both (i.e Passed in one but failed in other) = 20 + 27 = 47
So total number = (47/100) *2500 = 1175
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Anothe soln:
Passed in A = 100-35 =65
Passed in B = 100-42=58
Passed in Both = 100-15 =85.
Passed only in A = 65-85= -20
Passed only in B =58-85= -27
So passed in either but not both = -47..
Since -sign doens't make sense here, take the absolute value here..
47% of 2500..
Anything wrong with this approach ??:)
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.