# CAT Practice : Number System

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How scientifically can you do trial-and-error for this question?

## Perfect Square

Q.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

Choice A. 3

## Detailed Solution

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.

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