SOLUTION: a positive integer when divided by 88 gives the remainder 61. what will be the remainder when the same number is divided by 11

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Question 1138625: a positive integer when divided by 88 gives the remainder 61. what will be the remainder when the same number is divided by 11
Answer by ikleyn(52756) About Me  (Show Source):
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Let "n" be that integer number.


We are given that  (n-61) is divisible by 88.


Hence,  (n-61) is divisible by 11.


It is the same as to say that ((n-55)-6) is divisible by 11.     (*)


Since 55 is divisible by 11, (*) implies that (n-6) is divisible by 11.


It means that the number n gives the remainder 6 when is divided by 11.


ANSWER.  The remainder when the same number is divided by 11 equals to 6.