How many integers between 1 and 500 inclusive are divisible by both 6 and 9, but not 4? (I know this applies the inclusion-exclusion principle, but how do I use it?)

Question

dumbcow · Answer

my guess is 14

dumbcow · Answer

there are 55 multiples of 9 
of those 27 are even
of those 14 are not divisible by 4

anonymous · Answer

@dumbcow the answer is 21 according to the answer key.

dumbcow · Answer

but to be divisible by both 6 and 9 ... it must be a multiple of 18

there are 27 multiples of 18 between 1-500
if you look at multiples of 18, every other one is divisible by 4

so how is answer 21 ??

raden · Answer

i got like @dumbcow have
18,36,54,72,...,486 ----> there are 27 numbers
36,72,108,144,...,468 ---> there are 13 numbers
so, 27-13=14

dumbcow · Answer

haha im not crazy ...answer key may be wrong :{

raden · Answer

haha... but, ur guess is right, u are the faster feeling :)