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Question

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

CAT 2021

A
12
CORRECT ANSWER WRONG ANSWER
B
11
CORRECT ANSWER WRONG ANSWER
C
10
CORRECT ANSWER WRONG ANSWER
D
9
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(B)

Explanatory Answer :

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}}