Clealry Stmt I and II by themselves are not sufficient.

Stmt I

N= 5Q+4
Different remainders possible

Stmt II

N = 6q+5

Different remainders possible

Together

Identify first number that gives a remainder of 4 when divided by 5 and a remainder of 5 when divided by 6

29

Find the lcm of 5 and 6 i.e 30

So numbers will follow the pattern 29+ 30q

29
59
89

If u notice all these leave a remainder of 14 when divided by 15

SUFF



Choose C

Any rule to identify 29 or just picking numbers? Tksvm

Not that I know of(since the 29 applies to this problem; it could very well be a different number for anothe problem but once u identify this number by trials then the lcm part is generic).

Identify first number that gives a remainder of 4 when divided by 5 and a remainder of 5 when divided by 6

This is by trials. All I did was keep adding 4 to ever multiple of 5 and see if it met the remainder when divided by 6 .

Hope this helps!

Regards,
CR