Question

A number when successively divided by 2, 3, 5 it leaves the respective remainders 1, 2 and 3. What will be the remainder if this number will be divided by 7?___ (type '0' if it is cannot be determined)

Answer 1

Write the divisors and remainders as given below

then solve it as follows
(((3 $\times$ 3) + 2) 2 + 1) = 23
or 3 $\times$ 3 = 9
9 + 2 = 11
11 $\times$ 2 = 22
22 + 1 = 23
So, the least possible number is 23 and the higher numbers can be obtained as (2 $\times$ 3 $\times$ 5)m + 23 = 30m + 23.
So the higher numbers are 53, 83, 113, 143, 173, 213, 333, . .. . etc.
But when we divide all these possible numbers by 7 we get the different remainders. So we can not conclude the single figure as a remainder.