CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

The question is from CAT Number Theory - Remainders. Two large numbers leave same remainder when divided by a three digit number. We need to find out the three digit number. A range of CAT questions can be asked based on Remainders. When we divide 24 pigeons into 5 groups, 4 are left out or remain. This is the remainder. When there is a question based on this idea in the exam, we have a CAT among the pigeons.

Question 13: The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?

1. 206
2. 256
3. 274
4. 189

Explanatory Answer

Method of solving this CAT Question from Number Theory - Remainders: Remember! The difference between the numbers too leave the same remainder!

Let N be the 3 digit number.
Let R be the remainder.
So, 573921 – R and 575713 – R will be divisible by N
This means the difference between them is also divisible by N.

Difference = (575713 – R – 573921 + R) is divisible by N
Or 1792 divisible by N
N can be 256 from the answer choices!

The question is "What is that 3 digit number?"

Hence the answer is 256.

Choice B is the correct answer.