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A={1, 2, 3, 4, 5} is given. If there are 1,2,…,n subsets o

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A={1, 2, 3, 4, 5} is given. If there are 1,2,…,n subsets o

by Max@Math Revolution » Sun Sep 01, 2019 9:10 pm
[GMAT math practice question]

A={1, 2, 3, 4, 5} is given. If there are 1,2,...,n subsets of A, let A1, A2 , A3 ,... , An be the sums of the elements of the corresponding subsets of A. What is A1+ A2,+ A3+... + An?

A. 200
B. 210
C. 230
D. 240
E. 250
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by Max@Math Revolution » Sun Sep 01, 2019 9:11 pm
=>

A has 2^5 = 32 subsets, so n = 32. Each element of A is contained in 2^{5-1} = 2^4 = 16 subsets of A (We fix one element and find the number of subsets of the remaining elements). So, A1 + A2 + A3 + ... + A32 = 16*(1+2+3+4+5) = 240.

Therefore, the answer is D.
Answer: D
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