Since N/2 leaves a remainder, N must be odd and ends with 1, 3, 5, 7, or 9.
N/5 also leaves a remainder, so N is not divisible by 5, so it does not end in 5.
The only correct choice is then 9, since
1 = 0•5 + 1 and 1 = 0•2 + 1
3 = 0•5 + 3 and 3 = 1•2 + 1
7 = 1•5 + 2 and 7 = 3•2 + 1
9 = 1•5 + 4 and 9 = 4•2 + 1
Alternatively, the given information is equivalent to saying
[tex]N\equiv 4\pmod5\\\\N\equiv1\pmod2[/tex]
Then you can use the Chinese remainder theorem to find N.
