Question

The sets Sx are defined as {x, X + 1, X + 2, X + 3,
x + 4) for x = 1, 2, 3, ... 80. How many of these sets
contain 6 or a multiple of 6?
(A) 65 (B) 66 (C) 59 (D) 60

Answer 1

There are 14 multiples of 6 till 84.

Since 5 consecutive no.s are chosen only one set in 6 consecutive sets will not have a multiple of 6. So till 78 sets there are

$78− \binom{78}{6} = 78 - 13 = 65$

sets containing 6 or multiples of 6.

$\sqrt[s]{79}$

does not contain any multiple of 6

$log_{s}(80)$

must contain a multiple of 6.

Answer =66 sets

hope it will help you mate ☺️☺️☺️