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A number of dacoits need to hole up in their hideout. The problem is that, as with many criminal groups, there are a number of personality conflicts that disallow certain members of the dacoit group from being in the hideout at the same time as certain other members. The personality issues of the bandits $\text{A, B, C, D, E, F, G,}$ and $\text{H}$ are illuminated by the following constraints:

  1. If $\text{D}$ is in the hideout, then $\text{E}$ is in the hideout.
  2. If $\text{E}$ is not in the hideout, then $\text{A}$ is in the hideout.
  3. If $\text{B}$ is not in the hideout, then $\text{C}$ is not in the hideout.
  4. If $\text{F}$ is in the hideout, then $\text{H}$ is not in the hideout.
  5. If $\text{A}$ is not in the hideout, then $\text{B}$ is in the hideout.

If there are seven people in the hideout, then who could potentially be outside of the hideout?

  1. $\text{G}$
  2. $\text{F}$
  3. $\text{A}$
  4. $\text{D}$
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Correct Answer: (B)

Explanation:

If there are seven people in the hideout, then who could potentially be outside of the hideout?

(B) The answer to this is $F$ or $H$. They cannot be in the hideout together, and there are only eight people in the game, so one of these two must be out.

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