Aptitude - Numbers - Discussion

Any other easy way?

Sorry ! I couldn't get it.......... please explain it in another way.

hello buddys!

I think the following could be one of the methods:

we know, dividend=divisor*quosent+remainder
divisor=d,quosen=1(if not given assume it to be 1)+remainder=r

so, 2272=d*1+r
875=d*1+r
since remainder are equal from the question,
r=2272-d -equ1
r=875-d -equ2
equ=equ2

2272-d=875-d
we get 1397 this our N.and sum of the digits 20.
becoz we r dealing with two equ same remainder, so divide it by 2.
i.e 20/2= 10.

I dont know whether is it wright but any ways am getting the answer.

Let us suppose that, 2272=x+r and 875=y+r then x-y=2272-875=1397 this is the difference between the two numbers. This 1397 should be completely divisible by divisor (as 1397 is free from remainder and is the actual difference between the (2272-r) & (875-r) hence should be completely divisible by the divisor. Now 1397=11*127. As divisor should be a 3 digit number, so 127 can be considered as the remainder which fulfills our criteria. Therefore sum of digits=1+2+7=10.

Lets take the remainder as x,

2272-x is the quotient which is divisible by n.

875-x is the quotient which is divisible by n.

[2272-x]-[875-x] = a number which is divisible by n.

= 1397.

The factors of 1397 are 11 and 127.

127 is n as it is a three digit number and fills all conditions.

1+2+7 = 10.

10 is the answer.

Please explain me how you get 1397 is 11 & 127?

We can 11*127 so we can get 1397.

But how we get 10.

@Shreyank by adding the digits of 127 (i e. , the 3-digit number).

As 2272 and 875 is divided by same number(x), obviously they are the factors of (x).

So when we subtract 2272-875 = 1397.

Now, this 1397 is also factor of (x).

Now just simply divide 1397 by options given in number.

i.e. (10, 11, 12, 13) then we find that 11 is the only number divisible by 1397.

Hence 1397/11 = 127 i.e. 11*127 = 1397.

1+2+7 = 10.

Why we are factorizing 1397?