The numbers $41,35,19,9,26,45,13,28$ are arranged in pairs so that the sum of the numbers in each pair is the same. The number paired with 13 is
(A) 45
(B) 28
(C) 35
(D) 26
(E) 41
Solution 1

The sum of all 8 numbers in the list is $41+35+19+9+26+45+13+28=216$.

When the 8 numbers are arranged in pairs, there are 4 pairs.

The sum of the numbers in each pair is the same, and so this sum is $\frac{216}{4}=54$.

Therefore, the number paired with 13 is $54-13=41$.

Note: We may confirm that $45+9=54,41+13=54,35+19=54$, and $28+26=54$.

## Solution 2

Since the sum of the numbers in each pair is the same, then the largest number in the list must be paired with the smallest number, the second largest with the second smallest, and so on. (Can you reason why this must be true?)

That is, the largest and smallest numbers in the list, 45 and 9 , must be paired.

The second largest and second smallest numbers, 41 and 13, must be paired, and so the number paired with 13 is 41 .

Note: We may confirm that $45+9=54,41+13=54,35+19=54$, and $28+26=54$.

ANSWER: (E)