Question

The digits of a two digit integer N are interchanged to form an integer K. Find all possibilities for N is odd and exceeds by more than 18

Answer 1

let t be the tens digit of N

let u be the units digit of N

10t + u = N

10u + t = K

N - K > 18

(10t + u) - (10u + t) > 18

10t + u - 10u - t > 18

9t - 9u > 18

t - u > 2

t > u + 2

Since t < 10, it must be that u < 7

since N is odd the unit digits u = 1 , 3 , 5 ,...

If u = 1, t > 3, then N = 41 , 51 , 61 , 71 , 81 , 91.

If u = 3, t > 5, so N = 63 , 73 , 83 , 93.

If u = 5, t > 7, so N = 85 , 95.