Question

How many natural number sets of the form $S_n=\{n-4,n-3,n-2,n-1,n,n+1,n+2,n+3,n+4\}$ (n is a natural number $\le$100) and the set does not contain 10 or any integral multiple of 10?

• A. 8
• B. 9
• C. 10
• D. 15

Answer 1

The correct option is C

10

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 $n\le 100$

No. of such numbers $=\frac{91-1}{10}+1=\frac{90}{10}+1=9+1=10$