reminder when divided by 2,5 and 10

[santham]

What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer.


Please help

IMOE

[clock60]

here i got B, my thinking
when n is divided by 2 it can give only two remaiders 1 or 0, for remaider 1 n is odd, and for remaider 0 (n is divisible by 2) n is even.so the problem asks does n odd or even
(1)n=5k+(2m+1), here k is integer, and (2m+1)-odd remaider,(note m here can equal 0 or 1 only)
so the value of n depends on the value of k, if k is odd, n is even, if k is even ,n is odd, for example
k=1, n=5+1=6-even divisible by 2
k=2, n=10+1=11, 11=2*5+1, remaider 1 if divisible by 2, so insuff
(2) n=10m+(2n+1)
2n+1 is always odd, 10m is always even, so n must be odd and gives remaider 1

[GMATGuruNY]

What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer.


Please help

IMOE

When an even integer is divided by 2, the remainder is 0.
When an odd integer is divided by 2, the remainder is 1.
Thus, to determine the remainder when n is divided by 2, we need to know whether n is even or odd.

Question rephrased: Is n even?

Statement 1: When n is divided by 5, the remainder is an odd integer.
n=6 works, because 6/5 = 1 R1.
n=11 works, because 11/5 = 2 R1.
Since n can be even or odd, insufficient.

Statement 2: When n is divided by 10, the remainder is an odd integer.
Thus, n = (multiple of 10) + (odd integer), so that when n is divided by 10, the remainder is an odd integer.
A multiple of 10 is even.
Thus, n = even + odd = odd.
Sufficient.

The correct answer is B.