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10 Aug 2009, 11:16
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Set T={2,7,9,18,36,72,144,288,576}. If all the subsets of T containing at least two elements are formed, and V is the set of the sums of the elements of these subsets, how many distinct elements does V have?
(A) 346 (B) 382 (C) 495 (C) 502 (D) 512 (E) none of these
(A) 346 (B) 382 (C) 495 (C) 502 (D) 512 (E) none of these
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11 Aug 2009, 10:05
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I think the answer is C but I'd wait for someone more experienced to chime in here and confirm before you take my answer as correct
. Seems like just a combinatorics problem that's asking how many different combos can be made of 2 or more numbers out of the set of 9 numbers. Each combo = one element of V since the elements of V are just the sums of each combo.
So C(9,2) + C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9)
You can take C(9,2) + C(9,3) + C(9,4) and multiply by 2 to get C(9,2) through C(9,7). The sum of C(9,2) through C(9,7) = 492. C(9,8) = 9 and C(9,9) = 1. Total = 502.
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