Question

Let "n" be the smallest positive integer, larger than 150, so that
the number "C25, is divisible by "C.so but it is not equal to it. The
sum of digits of "n" is?

Answer 1

Answer:

12

Step-by-step explanation:

if u got the ans no problem

Answer 2

given a for smallest positive integer after $150$ of the given form , find the integer

Explanation:

1. for the given smallest integer 'n'  greater than $150$ and three doigts of the form  '$C25$' then we have,                                                                                     [tex]n=C25\ \ and\ \ n>150 \\ n=100C+25\ \ and\ \ n>150\\ 100C+25>150\\ C>1.25\ \ \\ =>C\geq 2[/tex]---(i)
2. given that $'C25'$ is divisible by C but not equal to it we get,                                  [tex]C25=100C+25\\ C25=100C+C(k)[/tex]               (here 'k' is some positive integer)                                                                                    
3. for given condition to be fulfilled 'C' must be an integer factor of $25$ ,                      $C(k)=25=1x5x5$
4. hence , possible cases are $(C=25, k=1)\ or\ (C=5,k=5)\ or\ (C=1,k=25)$                                               comparing these with (i) we get possible values of 'C', $C=25 ,\ 5$                      
5. now we have , $n=100C+25$   therefore,                                                                                   [tex]C=5\ \ \ \ ->n=500+25=525\\ C=25\ \ \ ->n=2500+25=2525[/tex]          
6. since, it is given that 'n' is smallest integer  we get, $n=525$  
7. Hence, sum of digits of 'n' is  $12$