CAT 2020 Quant Question [Slot 1] with Solution 14

The sum of possible even digit numbers in the form aabb is \(1100 + 1122 + 1144 + 1166 + 1188 + 2200 + 2222 + 2288 +  \ldots .9900 + 9922 + 9988\) i.e. \((45\) numbers)

\( \Rightarrow 1100 + 1100 + 1100 + 1100 + 1100 + 22 + 44 + 66 + 88 + 2200 + 2200 + 2200 + 2200 + 2200 + 22 + 44 + 66 + 88 +  \ldots  \ldots  + 9900 + 9900 + 9900 + 990 + 9900 + 22 + 44 + 66 + 88\)

\( \Rightarrow 5(1100 + 2200 +  \ldots .9900) + 9(22 + 44 + 66 + 88)5 \times 1100(1 + 2 +  \ldots  \ldots 9) + 9 \times 22(1 + 2 + 3 + 4)\)

\( \Rightarrow 5500(45) + 45 \times 44 = 45(5544)\)

Hence mean =5544