Divisibility, Maths Olympiad

Question

A series of bus tickets are labelled using all the numbers from 00000 through 99999. A girl collected all the tickets whose numbers are divisible by 78 and a boy collected all the tickets whose numbers are divisible by 77, but not by 78. How many more tickets did the girl collect?

Answer 1

99999 / 77 = 1298.69

99999 / 78 = 1282.03

You can ignore the decimals since you are only looking for how many multiples of the number there are in 99999.

Now the question is, how many numbers are divisible by 78 and 77. If we multiply 77 & 78, we know the common denominator of all integers that are divisible by both 78 & 77.

77 * 78 = 6006

99999 / 6006 = 16.65

Thus, you have the following!

The girl collected 1282

The boy collected 1298 - 16 = 1282

The boy & girl collected the same amount of numbers...