madcowudub wrote:

I found this question online.

At a club, there can be a number of 10-40 people. If 3 people sit at one table, then the remainding people can fit with 4 per table. If every 3 people sit on one table, then the remainding people can fit 5 per table. The question is: if 6 people sit per table, one table will not be able to be full, how many people can sit on that one table that isn't full?

the answer is 5. I'm not sure how this answer was reached. please help.

There are 10-40 people

1st condition is 4*a+3 (where a is the # of people sitting/table)

2nd condition is 5*b+3 (where b is the # of people sitting/table)

But bothe trhe total are equal

4*a+3 = 5*b+3

This can happen

when a=5 and b=4

OR

when a=10 and b=8 (but this cannot happen 'cos the max # of people is 40 and we cannot exeed that #)

4*10+3 = 43 (so ruled out)

So there are only 23 people

Now coming to the 3rd condition

6*c+d = 23 where d is the spill over people on the last table left

we have c=1 d=17

c=2 and d=11

c=3 and d=5

here d cannot be 6 or more (since this table has <6)

so the answer is 5