Aptitude - Numbers - Discussion

2272 - 875 = 1397 which is divisible by 11.
i.e. , 1397 = 11 X 127.
so, 1+2+7 = 10.

@All.

Here is the solution.

2272-R=0(mod N).
875-R=0(mod N).
2272-875=0(mod N).
1397=0(mod N).

So, any factor of 1397 can be the answer for N which 127 will be correct according to the question given (3digit numbers).

1+2+7=10.

Here we need to find the sum of the digits of the required 3-digit number.
As the given two numbers when divided by 3-digit numbers give the same remainder then that means when we find the difference between them then that difference will be divisible by that three-digit number.

So, we will first find the difference between the given numbers, i.e. 2272 and 875.

Difference=2272-875=1397 --->(1)

1397 will be divisible by a three-digit number i.e. N.
.
We know that the factors of the number 1397 are 11 and 127.
The only three-digit number which has a factor of 1397 is 127.
So, we can say that the value of the three-digit number i.e. N.
It's equal to 127.
Now, we will find the sum of the digits of the N.
The sum of the digits of N.
=1+2+7=10.
Hence, the correct option is option A.

Where did 11 and 127 comes from?

Please explain.

2272-875 = 1397 difference,
1397/11 = 127 divisible by 11,
1+2+7 = 10.

a=np+r
2272 = np + r ----------> (1)
b=nq+r
875=nq+r --------------> (2).

Subtracting (1)-(2).
2272-875 = n(p-q),
1397 = n(p-q),
1397 is only divisible by 11,
1397 = 11*127.

Hence n=127,
p-q = 11,
1+2+7=10.

2272 = N*Q1 + R -->eq1.
875 = N*Q2 + R -->eq2.
2272 - 875 = N(Q1-Q2) -->eq1 - eq2.
1397 = N(Q1-Q2) -->eq3.

Since there is no remainder in eq3, so 1397 is completely divisible by N.
Therefore, N should be a factor of 1397.
Factors of 1397 = 11 and 127.
Since N should be a 3 - digit number. Therefore N = 127.
Hence answer = sum of digits of N = 1 + 2 + 7 = 10.

Thank you @Queeen.

2272-875 = 1397.
1397/11 = 127.
1+2+7 = 10.

Both leaving same remainder(let Remainder is R) hence,
2272-R and 875-R Both are completely divisible by number.

Their difference will also divisible by the number,
(2272-R)-(875-R) = 1397.

Factors of 1397 = 11*127.
Asked for 3 Digit number.
Hence sum of digits is 1+2+7 = 10.