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GMATClub is a forum where people can participate in GMAT discussion. The forum is either doing well or badly, a status that totally depends on the activity in the forum. A group of GMATClub forum's members discovered that if Paul appears and actively posts messages, the forum discussion goes well. The members also found out that whenever Prae shows up to post messages, Paul is completely absent from the forum.
If the above statements are true, which of the following must also be true?
(A) If Prae does not show up, Paul must be actively posting messages.
(B) The appearence of Prae in the forum is sufficient for Paul to be actively posting messages.
(C) Either Paul's appearence is necessary for Prae to post messages or Prae's appearence causes the forum discussion to go badly.
(D) Prae's appearence is necessary for Paul's appearence.
(E) Prae shows up to post messages only if Paul appears.
Here is the OA.
Let
A = Paul appears and actively posts messages
B = forum discussion goes well
C = Prae shows up to post messages
~A = Paul is completely absent
~B = forum discussion to go badly
~C = Prae does not show up
According to the stem
A->B
C->~A
Following the answer choices
(A) If Prae does not show up, Paul must be actively posting messages.
~C -> A
conflict
(B) The appearence of Prae in the forum is sufficient for Paul to be actively posting messages.
C is sufficient for A
conflict
(C) Either Paul's appearence is necessary for Prae to post messages or Prae's appearence causes the forum discussion to go badly.
(A is necessary for C) OR (C -> ~B)
FALSE or TRUE = TRUE
correct
(D) Prae's appearence is necessary for Paul's appearence.
C is necessary for A
conflict
(E) Prae shows up to post messages only if Paul appears.
C only if A
conflict