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Lê Quốc Trần Anh Coordinator

12/03/2018 at 11:44
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If the digits 7, 8, 2, 3 and 0 are used, each exactly once, to form a three-digit positive integer and a two-digit positive integer that differ by exactly 288, what is the sum of the three-digit integer and the two-digit integer?



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    Lê Anh Duy 12/03/2018 at 13:02

    Name the 2 numbers are abc and de

    abc - de = 288

    => c - e = 8

    => (c;e) = (8;0),(0;2)

    C1: c = 8; e = 0

    => ab8 - c0 = 288

    => b - c = 8

    => IMPOSSIBLE

    C2: c = 0; e = 2

    => b - (d + 1) = 8

    => b = 7; d = 9

    => a = 3

    => abc + de = 370 + 92 = 462

    Lê Quốc Trần Anh selected this answer.


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