KVPY SA Exam 2014 Question Paper

100000 ≤ ababab < 1000000
$\le {10}^5\mathit{a}+{10}^4\mathit{b}+{10}^3\mathit{a}+100\mathit{b}+10\mathit{a}+\mathit{b}$
$\le \mathit{a}\left({10}^5+{10}^3+10\right)+\mathit{b}\left({10}^4+{10}^2+1\right)$ $\le 1000000$
$100000\le \left({10}^4+{10}^2+1\right)\left(10\mathit{a}+\mathit{b}\right)$
100000 ≤ 10101(ab) < 1000000
9.9 ≤ ab < 99
'ab' number can be obtained as product of ordered pairs
(2, 5); (2, 11); (2, 17); (2, 19); (2, 23); (2, 29); (2, 31); (2, 41); (2, 43); (2, 47); (5, 11); (5, 17); (5, 19)
Total numbers = 13