GMAT TIGER wrote:
q : A certain shelf holds less than 50 books . what is the number of books in the shelf?
1. books in the shelf can be divided into some stacks of 3 books each , with 2 left over.
2. books in the shelf can be divided into some stacks of 7 books each , with 3 left over
E. n could be 17 or 38.
I had to write out all the possibilities to figure it out...how did you do it?
n = number of books
1. n = 3m + 2
2. n = 7k+3
reminder when divided by 7 is 3, which is 1 more than the reminder (2) when divided by 3. so look for all the possibilities that are multiples of 7 plus 1 i.e. 7k + 1. this must be a multiple of 3.
3m +2 = 7k+3
3m = 7k+1
solve for the above eq. when m = 5, k = 2. when m = 12, k = 5.
then find n in each cases...