A number when divided by 12 gave a remainder 8. When the same number is divided by 48,the number of possible remainders will be,

Question

be 5

Answer 1

Let the number be n = 12 m + 8, \(m\in Z\) 

(i) m = 0, then n = 8, \(\frac n {48} \) gives remainder 8.

(ii) m = 1, then n  = 20, \(\frac n {48} \) gives 20 as remainder.

(iii) m = 2, then n = 32, \(\frac n {48} \) gives 32 as remainder.

(iv) m = 3, then n = 44, \(\frac n {48} \) gives 44  as remainder.

(v) m = 4, then n = 56, \(\frac n {48} \) gives 8  as remainder.

Hence, when n is divides by 48 then possible remainder are 8, 20, 32 or 44.