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Tough Percentage Puzzle

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  • 19-10-2009 12:57pm
    #1
    clartharlear
    Registered Users Posts: 489 ✭✭


    At college, 70% of the students studied Maths, 75% studied English, 85% studied French and 80% studied German.
    What percentage at least must have studied all 4?

    Initially, you’d think that it would be 70% AND 75% AND 85% AND 80%, which would give you 37.5%, but that doesn’t take into account that doing one subject doesn’t have any effect on whether any of the other subjects are done.

    I’ve seen another solution here, but I don’t find it convincing, though I believe the numerical answer.
    70 +75 + 85+ 80 = 310
    310 ÷ 3 = 100 remainder 10
    3 subjects each student, 10 at least 4

    I’ve been trying to draw Venn diagrams and Karnaugh maps with 4 variables where the outcome is F = ABCD, but I don’t know how to work that with the percentages.

    Help would be much appreciated!
    Tagged:


Comments

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    #2
    orourkeda
    Closed Accounts Posts: 17,918 ✭✭✭✭orourkeda


    http://www.britishblogs.co.uk/images/449592.jpg


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    #3
    The Thinker
    Registered Users Posts: 19 ✭The Thinker


    Hi,
    Probably a bit late with this, only spotted it today.
    30% didn't study Maths
    25% didn't study English
    15% didn't study French
    20% didn't study German

    This leaves 10% of students who must have studied all 4 ???


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    #4
    betterlife
    Closed Accounts Posts: 10 ✭betterlife


    The Thinker wrote: »
    Hi,
    Probably a bit late with this, only spotted it today.
    30% didn't study Maths
    25% didn't study English
    15% didn't study French
    20% didn't study German

    This leaves 10% of students who must have studied all 4 ???

    You've got a point there.


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    #5
    clartharlear
    Registered Users Posts: 489 ✭✭clartharlear


    The Thinker wrote: »
    Hi,
    Probably a bit late with this, only spotted it today.
    30% didn't study Maths
    25% didn't study English
    15% didn't study French
    20% didn't study German

    This leaves 10% of students who must have studied all 4 ???
    Yes, that's exactly it. Thanks and well done!


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