Q3 FACTORS - MULTIPLES
Consider the sets Tn={n,n+1,n+2,n+3,n+4},
where n = 1, 2, 3,..., 96. How many of these sets contain 6 or any integral
multiple thereof (i.e., any one of the
numbers 6,
12, 18,...)?
(1) 80
(2) 81
(3) 82
(4) 83
(1) 80
(2) 81
(3) 82
(4) 83
Consider the sets Tn = {n, n + 1, n +2, n + 3, n + 4), where n = 1
T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets.
We have (96-6)/6+1=16 such multiples.
So, final number of sets is 16*5=80
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