Numbers-11 (CAT-2004)

Suppose n is an integer such that the sum of digits of n is 2,
and 10¹⁰ < n < 10¹¹. The number of different values for n is:

 (1) 11      (2) 10     (3) 9       (4) 8
For Answer Click on "Read more" below:

Solution:

Given that, 10¹⁰ < n < 10¹¹

=> n is a 11 digit number.

“The sum of digits of n is 2” is possible only in two cases

Case-1:

One digit being 2 and all remaining 10 digits being 0’s:

The only possible number is => 20000000000

Case-2:

Two digits being 1’s and all remaining 9 digits being 0’s:

First digit must be 1 and second one can be placed in one of the remaining 10 positions

=> possible 10 different numbers:

11000000000, 10100000000, 10010000000, 10001000000, 10000100000, 10000010000, 10000001000, 10000000100, 10000000010, 10000000001

In total, there are 11 possible numbers

Answer (1)