diebeatsthegmat wrote:What is the sum of the remainders when n positive integers were divided by 2?
(1) The sum of n numbers is an even number.
(2) Eight numbers are odd.

[spoiler]why the answer is B? i am not convinced with the answer because we dont know how many numbers is n. n can have 9 or 10 numbers, and according to statement 2, ne has 8 odd numbers and 2 even numbers thus its remainders might be zero and 1 so insufficient.
statement 1: sum of n number is even... those numbers could has even numbers of odd numbers or even numbers of odd numbers + some even numbers.... sp insufficient
the answer should be E[/spoiler]

experts, please help me

When an even integer is divided by 2, remainder = 0:
2/2 = 1 R0.
100/2 = 50 R0.

When an odd integer is divided by 2, remainder = 1:
1/2 = 0 R1.
3/2 = 1 R1.
101/2 = 50 R1.

Thus:
Each even integer will not increase or decrease the sum of the remainders.
Each odd integer will increase the sum of the remainders by 1.

So the question can be rephrased: how many of the n integers are odd?

Statement 1: Sum of the n numbers is even
The numbers could be {2,4}, since 2+4 = 6.
Sum of the remainders = 0+0 = 0.

The numbers could be {3,5}, since 3+5 = 8.
Sum of the remainders = 1+1 = 2.

Insufficient. No way to tell how many of the integers are odd.

Statement 2: Eight numbers are odd
If there are 8 odd integers, the sum of the remainders = 1+1+1+1+1+1+1+1 = 8.
Sufficient.

The correct answer is B.