Question

A servant bought 150 balls but he lost some of them. When asked how many balls has been lost, he gave the following response: If counted in pairs, one will remain; If counted in threes, two will remain; If counted in fours, three will remain; If counted in fives, four will remain; If counted in sixes, five will remain; If counted in sevens, nothing will remain;

Answer 1

no. of balls = 150
If counted in pairs, 1 will remain.So the required no. will be an odd no.
If counted in three, 2 will remain.So the required no. is 3n+2
If counted in five,4 will remain.So the required must ends up with 9(since end no. can possibly be 4 and 5, and 4 is an even no.)
The required no is divisible by 7 and ends up with 9. Possible numbers are 49 and 119.
49=3 multiplied by 16+1 which is not equal to 3n+2.
Hence the required no. is 119.