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In the diagram, each of a, b, c, … ,g represents one of th

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by Max@Math Revolution » Thu Jul 11, 2019 11:37 pm
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[GMAT math practice question]

In the diagram, each of a, b, c, … ,g represents one of the numbers 1, 2, 3,… and 7, with no repetition. These values correspond to the number of elements in each part of the sets. If sets A, B and C have the same number of elements and the sum of the numbers of elements of A, B and C is as small as possible, find the value of b+d+f.

A. 5
B. 7
C. 9
D. 11
E. 13

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by Max@Math Revolution » Sun Jul 14, 2019 4:54 pm
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The number of elements in set A is a + b + c + d. The number in set B is b + c + e + f, and the number of elements in set C is c + d + f + g. The sum of the sizes of these three sets is then a + 2b + 3c + 2d + e + 2f + g.

To minimise this total, c must have the smallest value as its coefficient is the largest. Thus, c = 1. The next smallest values must be given to b, d, and f as they have coefficients of 2. Thus, b,d and f are chosen from 2, 3 and 4.
It follows that b + d + f = 2 + 3 + 4 = 9.

Therefore, the answer is C.
Answer: C
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