Çözüldü Divisibility - Odd and Even Numbers

Konusu 'TOEFL - IELTS - SAT - GRE Hazırlık' forumundadır ve Honore tarafından 22 Eylül 2019 başlatılmıştır.

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  1. Honore

    Honore Yönetici

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    How many different values larger than 10 can the remainder hold after a three-digit number xy5 is divided by 26?
    https://scontent-otp1-1.xx.fbcdn.ne...=e3fefe6db7103cb8580200a4da0696c2&oe=5E359F31
    https://www.facebook.com/photo.php?...&set=gm.1659892637481606&type=3&theater&ifg=1
    [Another solution by a math teacher Mr. Erkan Akça: The number of the two-digit odd numbers less than 26, because dividend (xy5) is odd, quotient multiplied by divisor (26) is even, so remainder must be odd.]

    Starting from the lowest xy5 number as 105 with the remainder 1 in increments of 10;
    115----11
    125----21
    135-----5 ( = 31 - 26)
    145----15
    155----25
    165-----9 ( = 35 - 26)
    175----19
    185-----3 ( = 29 - 26)
    195----13
    205----23
    215-----7 ( = 33 - 26)
    225----17
    *****************
    235-----1 ( = 27 - 26)
    ...cycles

    So, only 8 numbers which are 11, 13, 15, 17, 19, 21, 23, 25.

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