Data Sufficiency

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.

Thanks.

from
(1) I find that remainders are odd when n=6, 8.... That is, when 6/5 remainder is 1 and 8/5, remainder is 3. Here, because these number are multiples of 2, remainder is 0 when they're divided by 2. Therefore, Sufficient.

from
(2) I find that remainders are odd when n=11, 13.... That is, when 11/10, remainder is 1 and 13/10, remainder is 3. Here, because these numbers give remainder of 1 when divided by 1, this is also sufficient.

So, i chose D.... But, the correct answer is B. What am I doing wrong?

For 1

the number could be

x = 5n + 1 = 5k +3

now depending on value of n these two expression can be odd or even

i.e put n = 1 n=2 and so remainder can be 0 or 1. Hence A is Insuff

but for 2 the expression 10j +1 will always be odd as 10j is always even hence remainder will always be 1 when divided by 2

Consider 1st Statement

n=6,8....As you said all these numbers are multiple of two and therefore they will have remainder as 0.

Consider the other situation. If n=11,13...

11/5=Remainder is 1....ODD

13/5=Remainder is 3...ODD

When you divide 11 or 13 by 2 you will get remainder as 1. So it is not Sufficient.

Your thinking on B is correct and hence the answer is B.

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.

E

Agree with cubicle.It has to be B