SOLUTION: folder contains less than 100 files. When the files are deleted in groups of five there are three leftover. When the files are deleted in groups of nine, there are six left over.

Question 1149008: folder contains less than 100 files. When the files are deleted in groups of five there
are three leftover. When the files are deleted in groups of nine, there are six left over. When
the files are deleted in groups of eleven there is only one left over. How many files are in
the folder?

Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
folder contains less than 100 files.
When the files are deleted in groups of five there are three leftover.
---> units digit is 3 or 8
=================================
When the files are deleted in groups of nine, there are six left over.
When the files are deleted in groups of eleven there is only one left over.
How many files are in the folder?
=================================
There's no algebraic solution, no formula.
Figure it out.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Let the number of files be N. Then

(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)

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.

It might go something like this....

We know from (2) that N is a multiple of 3.

(1) then tells us that a must be a multiple of 3.

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

N is the number in that list that is 1 more than a multiple of 11: 78.

ANSWER: N = 78

RELATED QUESTIONS
A filing cabinet contains 200 standard files. When 50 files have been stored in the... (answered by OmniMaestra)
dangerous computer virus attacks a folder consisting of 250 files. Files are affected by... (answered by ewatrrr)
A dangerous computer virus attacks a folder consisting of 250 files. Files are affected (answered by Edwin McCravy)
Jack and Jill each own a collection of mp3 files. Jill has six mp3 files less than three... (answered by lwsshak3)
The computer virus attacks a folder consisting of 28 files. The virus corrupts the files... (answered by ikleyn)
Data files on computers have sizes measured in megabytes. When files are sent from one... (answered by robertb)
There are files, staplers and books in a box. {{{3/5}}} of the items are files.... (answered by ptaylor)
Assume that only 31% of music files downloaded from Web sites in 2009 were paid for.... (answered by ikleyn)
Suzy caught 16 files in a week. The next week she caught only 9 files. What was the... (answered by macston)