Double a and Double b
Number Theory
Level
1
If aabb is four digit perfect square number then, a+b = ? Note a is not equal to b
9
11
33
10
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aabb = 1000a+100a+10b+b = 1100a+11b = 11(100a+b). Since aabb is a perfect square, 100a+b must have a factor of 11. To try to find the desired factor,11: 100a+b = 99a+(a+b) = 11(9a+(a+b)/11). So (a+b) must be divisible by 11. Hence (a+b) = 11 could be the only ans from the given options. Note that (a+b) can in principle be any multiple of 11(not any but at least some).