How many counting numbers less than 100 have an EVEN remainder when divided by 5 and an ODD remainder when divided by 7?
even multiples of 5 end in 0. So, you want numbers ending in 2 or 4
odd multiples of 5 end in 5, so you want numbers ending in 7 or 9
Now look at the list of even remainders when divided by 7:
1,3,5,8,10,12,15,17,19,22,24,26,29,31,33,36,38,40,43,45,47,...
So, how many of the second list end in 2,4,7,9?