GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 8

A 4-digit number of the form aabb is a perfect square. What is the value of a – b ?
(A) 3
(B) 2
(C) 1
(D) 4

Answer: (A)
Explanation: 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.

Hence the answer is “3”.

Option (A) is correct.
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