Question

For each non-empty subset of {1, 2, 3, 4, 5, 6, 7} arrange the member in decreasing order with alternate '+' and '–' signs starting with '+' sign and take the sum. {e.g. for the subset {5} we get the sum = 5. For the subset {6, 3, 1} we get the sum = 6 – 3 + 1 = 4.} Find the sum of all resulting numbers.

(A) 996

(B) 280

(C) 448

(D) 224

Answer 1

Correct option (C) 448

Explanation:

7 occurs (6C0 + 6C1 ......... + 6C6) times with '+' sign.

6 occurs (5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 ) times with '+' sign and occurs (5C0 + 5C1 ...... + 5C5 ) times with '–' sign.

And so on

Hence the required sum = 7 × 26 = 448