Question
How many natural number sets of the form Sn={n−4,n−3,n−2,n−1,n,n+1,n+2,n+3,n+4} (n is a natural number ≤100) and the set does not contain 10 or any integral multiple of 10?
Answer: Option C
:
C
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C
To get a set of 9 numbers, none of which are divisible by 10, we need to consider the lowest valued number in the set to have a value 1 above the divisor of 10. 0 is a divisor, one above that will be 1 and the lowest valued number in the set is n-4.
So, n-4=1. Now subsequent sets will occur in an AP with a common difference of 10.
1,11,21,31,41.....91 as n≤100
No. of such numbers =91−110+1=9010+1=9+1=10
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