Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
A
2
B
4
C
0
D
1
E
3
Correct Answer: 1
Any four digit number in which first two digits are equal and last two digits are also equal will be in the form 11 × (11a + b) i.e. it will be the multiple of 11 like 1122, 3366, 2244, . . . .Now, let the required number be aabb.
Since aabb is a perfect square, the only pair of a and b that satisfy the above mentioned condition is a = 7 and b = 4Hence, 7744 is a perfect square
