Question

A three digit number was divided successively in order by 4, 5 and 6 leaving out the remainders. the remainders were respectively 2, 3 and 4. how many such three digit numbers are possible?

Answer 1

Answer:

There are 7 possible three digits numbers.

Explanation :

When a three digit number is divided by

4,5,6 successively, the final quotient will be

a single digit (as 4*5*6 = 120 and the max

three digit number 999 is not more than

9*120).

Let the number be x and the quotient after

division by 4 be a and the quotient after

division by 5 be b and the quotient after

division by 6 be c.

Then, x = 4a+2,

a = 5b +3

b = 6c + 4.

Now start with c=1, b=10, a=53, x=214

when c=2, b=16, a=83, x=334,

c=3, b=22, a=113, x=454 and so on with

an increment of 120. Thus the 3 digit

numbers possible are 214, 334, 454, 574,

694, 814, 934.

The answer is 7 such numbers are

possible.