11. If a visitor to the exhibition enters no room more often than necessary to visit all of the rooms and then leaves the exhibition, which of the following rooms must the visitor enter exactly twice?
(A) R (B) S (C) T (D) X (E) Y
12. After stopping to rest in Z, a visitor goes from Z to T, passing through no more rooms than necessary. On reaching T, the visitor will have passed through a total of how many rooms (counting neither Z nor T) since the rest stop?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
13. Which of the following proposed new doorways would make it possible for a visitor to begin at R and visit all the rest of the rooms, arriving last at Z, without having entered any of the rooms in the exhibition twice?
(A) R-U (B) S-Z (C) T-U (D) U-Y
(E) U-Z
Questions 14-18
Each perfume made by a manufacturer is a mixture of two or more essences selected from a stock of exactly five different essences labeled F, G, H, J, and K. The manufacturer has learned that a formula for a perfume is acceptable if and only if it does not violate any of the rules listed below.
If the perfume contains F, it must also contain H, and there must be twice as much H as F.
If the perfume contains G, it must also contain J, and the amount of J must equal the amount of G.
H cannot be used in combination with J.
J cannot be used in combination with K.
If the perfume contains K, the amount of K must be greater than the total amount of the other essence or essences used.
14. Which of the following is an acceptable formula for a perfume?
(A) One part F, one part K
(B) Two parts G, two parts F