Francesca chooses an integer from the list $-4,-3,-2,-1,0,1,2,3,4,5,6$ and then a second integer that is larger than the first. How many such pairs of integers can she choose so that the sum of the pair is 3 ?
(A) 8
(B) 5
(C) 4
(D) 7
(E) 6
If Francesca first chooses -4, then there is no integer that she may choose second to give a sum of 3 (the largest integer in the list is 6 , and $-4+6=2$ ).

If she first chooses -3 , she may then choose 6 to give a sum of 3 .

If she first chooses -2 , she may then choose 5 to give a sum of 3 .

If she first chooses -1 , she may then choose 4 second to give a sum of 3 .

If she first chooses 0 , she may then choose 3 to give a sum of 3 .

If she first chooses 1 , she may then choose 2 to give a sum of 3 .

If Francesca first chooses 2 (or any integer larger than 2), then there is no integer that she may choose second to give a sum of 3 (the second integer must be larger than the first, and so the sum will be larger than 5 ).

There are 5 such pairs of integers that Francesca can choose so that the sum is 3 .

ANSWER: (B)