<PRE><B>Question 1149008</B>
&lt;br&gt;
Let the number of files be N.  Then&lt;br&gt;
(1) N = 5a+3  for some integer a  (N is 3 more than a multiple of 5)
(2) N = 9b+6  for some integer b  (N is 6 more than a multiple of 9)
(3) N = 11c+1 for some integer c  (N is 1 more than a multiple of 11)&lt;br&gt;
There are formal mathematical methods for solving problems like this, given the remainders when the number is divided by different integers.  But with the small divisors, and with the small value of N, the answer can be obtained using a bit of logical analysis.&lt;br&gt;
It might go something like this....&lt;br&gt;
We know from (2) that N is a multiple of 3.&lt;br&gt;
(1) then tells us that a must be a multiple of 3.&lt;br&gt;
So make a list of all the numbers less than 100 of the form 5a+3 where a is a multiple of 3:
18, 33, 48, 63, 78, 93&lt;br&gt;
N is the number in that list that is 1 more than a multiple of 11: 78.&lt;br&gt;
ANSWER: N = 78&lt;br&gt;
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