Question

# If aabb is a four digit number and also a perfect square then the value of a+b is

CAT 2021

A
B
C
D
##### 9
Solution

Correct option is

(B)

Number aabb can be written in expanded from as

aabb = 1000a + 100a + 10b + b = 1100a + 11b = 11(100a + b)

For aabb to be a perfect square, 100a + b should be of the form 11n^2

, where n is a natural number.

∴ aabb = 11 × 11 × $n^{^{2}}$

When n = 4,

11 × 11 × $n^{^{2}}$

= 121 × 16 = 1936. This is not in the form aabb.

When n = 5,

11 × 11 × $n^{^{2}}$

= 121 × 25 = 3025. This is not in the form aabb.

When n = 6,

11 × 11 × $n^{^{2}}$

= 121 × 36 = 4356. This is not in the form aabb.

when n = 7,

11 × 11 × $n^{^{2}}$