CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

The question is about different Perfect Squares. Format of a perfect square is given, we need to do an algebraic action using the format. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 3: A 4-digit number of the form aabb is a perfect square. What is the value of a - b?

1. 3
2. 2
3. 4
4. 1

Explanatory Answer

Method of solving this CAT Question from Number Theory - Digits: How scientifically can you do trial-and-error for this question?

A number of the form aabb has to be a multiple of 11.
So, it is the square of either 11 or 22 or 33 or...so on up to 99.
88² = 7744.
This is the only solution possible. Most of these trial and error questions need to be narrowed down a little bit before we can look for the solution. That narrowing down is critical. In this case, we should look for multiples of 11.

The question is "A 4-digit number of the form aabb is a perfect square. What is the value of a - b?"

Hence the answer is "3"

Choice A is the correct answer.