Pg 635 (567) - Q21
6 distinct sums can be obtained by adding -3 to each of the 6 other
numbers. This takes care of the negative numbers, because adding
either -2 or -1 to any other number would obtain a sum already obtained
using -3 and the other numbers. You can obtain 3 distinct sums by
adding 0 to each of the positive numbers. Another distinct
sum can be obtained by adding 1+3, and finally one more with 2+3.
There is thus a total of 11, which is choice B. Another way of seeing
it is that the smallest sum you can obtain is -5 (-3 + -2), while the largest
sum you can get is 5 (2 + 3). There are a total of
11 numbers between -5 and 5, inclusive, and each can be obtained
using a combination of 2 numbers.