Simple question about remaings

[imyhpark]

F(n) is Remaings when "n" is divided by k. Is K>10 ( n,k are integers)

1) f(k+32) =8
2) f(k+42) =6

pls explain why OA is a

[liferocks]

we can write the relation like this
n=mK+f(n)
now from 1,putting n=K+32 and simplyfying we get
km=k+24
or,K=24/(m-1)
since k is integer m-1 has to be a divisor of 24..ie one of 1,24,2,12,3,8,4 and 6
among these only m-1=24 satisfies relation km=k+24
so sufficient

proceeding similarly we get from condition2
km=K+36
or,k=36/(m-1)
factors of 36 are 1,2,3,4,6,9,12,18,36
here for m-1 we get two values(36 and 6 )which satisfies km=k+36
so insufficient

ans is A
now while checking for the factors ,its obvious that the first(24 for cond1 and 36 for 2) will satisfy the relation,so i have checked with only those factors which has values less than 10 to speed up.

[dxgamez]

Still not getting the formula for remainders.

Can the formula be used for all remainder qns?

[liferocks]

this is the general relation
dividend=divisor*quotient+reminder
you can use this for any reminder related problem.
does it clear the confusion?

[dxgamez]

Right. Much clearer. Thanks!