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6 October, 05:16

Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ... ?

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  1. 6 October, 07:37
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    The answer is 60.

    Let A be the number of radios with digital tuners and let B be the number of radios with CD players.

    The total number of radios is A∪B. It consists of both A radios and B radios, but however, radios with both digital tuners and CD players (A∩B) must be excluded from that number (either way they will be counted twice):

    A∪B = A + B - A∩B

    A∪B = 100

    A = 70

    B = 90

    A∩B = ?

    100 = 70 + 90 - A∩B

    100 = 160 - A∩B

    A∩B = 160 - 100

    A∩B = 60
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