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7 December, 05:44

A woman with a basket of eggs finds that if she removes the eggs from the basket at 5 or 11 at a time, there is always 1 egg left. however if she removes the eggs 7 at a time there are no eggs left. If the basket holds up to 100 eggs, how many eggs does she have

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  1. 7 December, 05:55
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    56

    Step-by-step explanation:

    I knew that the answer would a multiple of 7, and be one more than a multiple of 5 and 1 more than a multiple of 11. I looked at the multiples of 7 to find one that was true for all of that.

    Proof that 56 is correct:

    First we will take 11 away until we have a remainder.

    56-11=45

    45-11=34

    34-11=23

    23-11=12

    12-11=1

    When we take a way 11 at a time there is always 1 egg left.

    Now check for the remainder when taking away 5.

    56-5=51

    51-5=46

    46-5=41

    41-5=36

    36-5=31

    ...

    6-5=1

    When we take a way 5 at a time there is always 1 egg left.

    56 is divisible by 7 so there will be no eggs left when removing 7 eggs at a time.
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