2018 · Q23
The sum of all possible products taken two at a time out of the numbers ± 1, ± 2, ± 3, ± 4 is
Elementary MathematicsNumber System
- A0
- B- 30
- C30
- D55
Explanation
For numbers x_1..x_8, the sum of all pairwise products equals ((sum x_i)^2 - sum x_i^2)/2. Here the sum is 0 and the sum of squares is 2(1 + 4 + 9 + 16) = 60, so the required sum is (0 - 60)/2 = -30. The stored key (A) is wrong; the correct value is -30. Hence option B.