If x is a positive integer, is x divided by 5 an odd integer?

X is a positive integer. If X is divided by 5, will the result be odd?

Statement 1: X contains only odd factors
If X = 25 then the factors are 5 and 5. All factors are odd. X/5 is 5, which is odd.
If X = 27 then the factors are 3 and 9 (or 3-3-3). All factors are odd. X/5 is 27/5 though, which is not even and not odd.
Not sufficient.

Statement 2: X is divisible by 5
If X is 5 then it is divisible by 5. X/5 is 1 which is odd.
If X is 10 then it is divisible by 5. X/5 is 2 which is even.
Not sufficient.

Both: X is divisible by 5 and contains only odd factors.
If X is divisible by 5 and contains only odd factors, then it cannot end in zero. So it can be 5, 15, 25, 35, 45, 55, etc.
X cannot be 10 or 20 because those numbers are both divisible by 2, which is an even factor.
It looks like the formula for all the numbers that meet the requirements is X=5(2n+1), or all the odd numbers of 5n.
Since X will always be odd, and odd/odd is always odd, then x/5 will be odd.
This is sufficient, the answer is C.

Very Simple

In order for x divided by 5 to be an odd integer x just has to be an odd multiple of 5- be careful- you need both statements in order to draw that conclusion

Start with easy statement 2.

25 is multiple of 5 that gives odd integer.
60 is a multiple of 5 that gives even integer. Insufficient.

Statement 1.

15 divided by 5 gives odd integer
21 divided by 5 doesn't give an integer. Insufficient.

1+2. It gives numbers like multiples of 5 with no 2 in it, viz. 15, 45 etc. Quotient is always odd Integer. Sufficient.

such an easy question, and yet its so good mind trick.