SOLUTION: a 2 digit number gives a remainder of 6 when divided by 10. it gives a remainder of 5 when divided by 7. find the greatest possible 2 digit number

Question 1107244: a 2 digit number gives a remainder of 6 when divided by 10. it gives a remainder of 5 when divided by 7. find the greatest possible 2 digit number
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
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96.

    Obviously, this 2-digit number is of the form N =x6, where x is the "tens" digit and 6 is the "ones" digit.


    Since "it gives a remainder of 5 when divided by 7", it means that  N-5 is divisible by 7.


    N-5 is the number of the form  x1  (referring to N = x6), i.e. N-5 is ended by "1".


    Among 2-digit numbers there are only TWO of the form x1 that are divisible by &. They are 21 and 91.


    91 is the largest, and it produces  N = 96.

Solved.

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