With all due respect to a lovely lady I know who works a problem like this one every week for real, here's my "submission."------

Mistresses Petra, Wendy, Noelle, Domina, and Estrella work in a local sessions house. Their availability is subject to the following constraints.

Wendy cannot work on Monday or Thursday.

Domina cannot work on Wednesday.

Estrella cannot work on Monday or Friday.

Noelle can work at any time.

Petra cannot work evenings.

Wendy can only work evenings.

Petra will not work on Wednesday if Noelle works on Thursday, and Noelle works on Thursday if Petra cannot work on Wednesday.

At any given time there are always three women available for sessions.

1. At which one of the following times can Wendy, Domina, and Estrella all be working?

(A) Monday morning

(B) Friday evening

(C) Tuesday evening

(D) Friday morning

(E) Wednesday morning

2. For which day will another lady need to be hired?

(A) Monday

(B) Tuesday

(C) Wednesday

(D) Thursday

(E) Friday

3. Which one of the following must be false?

(A) Domina does not work on Tuesday.

(B) Estrella does not work on Tuesday morning.

(C) Petra works every day of the week except Wednesday.

(D) Noelle works every day of the week except Wednesday.

(E) Domina works every day of the week except Wednesday.

4. If Noelle does not work on Thursday, then which one of the following must be true?

(A) Petra works Tuesday morning.

(B) Domina works Tuesday morning.

(C) Estrella works on Tuesday.

(D) Petra works on Wednesday.

(E) Wendy works on Tuesday morning.

These are real (modeled after real GRE questions)! Scroll down to see the answers ONLY after you've worked them out yourself!

Answers:

1) All three can work on Tuesday night. The answer is (C).

2) Domina and Noelle are the only people who can work Monday evenings, and three women are always available for sessions, so extra help will be needed for Monday evenings. The answer is (A).

3) The condition "Petra will not work on Wednesday if Noelle works on Thursday, and Noelle works on Thursday if Petra cannot work on Wednesday" can be symbolized as (P_W)<-->(N=TH). Now, if Noelle works every day of the week, except Wednesday, then in particular she works Thursday. So from the condition (P_W)<-->(N=TH), we know that Petra cannot work on Wednesday. But this leaves only Noelle and Estrella to work Wednesday mornings. Hence the answer is (D).

(4) If you remember to think of an if-and-only-if statement as an equality, then this will be an easy problem. Negating both sides of the condition(P_W)<-->(N=TH) gives (P=W)<-->(N_TH). This tells us that Petra must work on Wednesday if Noelle does not work on Thursday. The answer, therefore, is (D).

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