There are 6 persons : A, B, C, D, E and F A has 3 items more than C D has 4 items less than B E has 6 items less than F C has 2 items more than E F has 3 items more than D Which one of the following figures can not be equal to the total number of items po

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Q: 3 (IAS/2005)
There are 6 persons : A, B, C, D, E and F
A has 3 items more than C
D has 4 items less than B
E has 6 items less than F
C has 2 items more than E
F has 3 items more than D
Which one of the following figures can not be equal to the total number of items possessed by all the 6 persons?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,5,11,2,7,5,2

keywords: 

{'total number': [0, 0, 3, 0], 'items': [3, 4, 8, 15], 'figures': [0, 0, 1, 1], 'persons': [4, 4, 9, 10]}

In the question, we are given relationships between the items that each of the six individuals own, but we aren`t given any absolute figures. It means that the total number of items can vary but will always maintain a certain pattern.

In taking the relationships into account, we find that we have:

- A = C+3

- D = B-4

- E = F-6

- C = E+2

- F = D+3

We can therefore combine all those to lead to B (since D, F, E and C can all lead back to B) which results in the equation B = B (A is not considered because it is just C + 3).

Therefore, the total number of items is a multiple of the number of items B has. On checking options, we learn the numbers 41, 47 and 58 each can be divisible by an integer, but 53 cannot be divisible without including a decimal; thus it cannot represent the total number of items owned by the six people. Therefore, the correct answer is 3, meaning 53 items.