S is the set of positive integers such that when divided by 2, 4, 5, 8 leaves remainders 1, 3, 4, 7.  How many integers between 0 and 100 belongs to set S?

2

LCM of 2, 4, 5, 8 = 40

Note: when different remainders left then, 'the difference b/w (2 & 1), (4 & 3), (5 & 4) and (8 & 7) = 1 is to be subtracted from the LCM'

Therefore,

S = 40K - 1

(i)  when K = 1,     S = 40 - 1 = 39

(ii) when K = 2,     S = 40 × 2 - 1 = 79

Only Two numbers are possible between 0 to 100