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Count Apples Basket Puzzle

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In a basket of apples, 
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there were five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket ?

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pnikam Expert Asked on 22nd August 2015 in Math Puzzles.
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    • 2 Answer(s)

    119

    Let the number of apples = X
    X / 2 => Remainder = 1
    X / 3 => Remainder = 2
    X / 4 => Remainder = 3
    X / 5 => Remainder = 4
    X / 6 => Remainder = 5
    X / 7 => Remainder = 0

    Therefore, X is divisible by 7.

    Whenever X is divided by any number less than 7, the remainder is 1 less than the divisor.
    => X + 1 is the LCM of 2, 3, 4, 5 and 6.

    Now LCM of 2, 3, 4, 5 and 6 = 60
    But 60 – 1 = 59 is not divisible by 7

    60 * 2 = 120
    120 – 1 = 119 which is divisible by 7

    This means that X + 1 = 120 or X = 119

    Number of minimum number of apples in the basket = 119

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    anikam Expert Answered on 22nd August 2015.
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    We know that the number of apples is divisible by 7 and we also know that when divided by a number less than 7 the remainder is 1 less than the divisor.
    So than means that if we had 1 more apple the remainder will be zero so that x+1 can be divided by 2,3,4,5,6 and x is divided by 7.
    The 1st number that meets all the conditions is 119

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    Moshe Expert Answered on 11th January 2023.
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