a. When divided by 7, there is a remainder of 1 b. When divided by 9, there is a remainder of 7 c. When divided by 11, there is a remainder of 10

Question

Find the smallest number that meets all of these conditions.

Answer 1

Start with the multiples of the given divisor, then add the remainder:

  For example:  multiples of 7 are:     7   14    21    28    35    42    49

                          +1                        8   15    22    29    36    43    50

 

Do that for 9 and for 11.

 

Now, the answer is the first value common to all three lists;

 7a+1:            8    15    22    29    36    43    50    57    64    71    78

 9b+7            16    25    34    43    52    61    70    79    88    97   106

11c+10          21    32    43    54    65    76    87    98   109   120

Answer 2

N=7a+1

N=9b+7

N=11c+10

7a=9b+6

7a=11c+10

a,b,c has to be positive integers, a>b>c,

C=3, b=4, a=6

N=43