Seven students-fourth-year students Kim and Lee. third-year students Pat and Robin: and second-year students Sandy, Tety and Val-and only those seven, are being assigned a rooms of equal size in a dormitory. Each room assigned must have either one or two or three students assigned to it and will accordingly be called either a single or a double or a triple. The seven students are assigned to moms in accordence with the following conditions:
Lio fourth-year student can be assigned to a triple.
No second-year student can be assigned to a single.
Lee and Pobin must not share the same room
Kim and Pat must share the same room.
1. Which one of the following is a combination of rooms to which the seven students could be assigned?
(A) two triples and one single (B) one triple and four singles (C) three doubles and a stngle (D) two doubles and three singles (E) one double and five singles
2. It the room assigned to Robin is a single, which one of the following could be true?
(A) There is exactly one double that has a second-year student assigned to it. (B) Lee is assigned to a stngle. (C) Sandy Fat and one other student are zseigned to a triple together. (D) Lixactly three of the rooms assigned to the students are singles (E) Exactly two of the rooms assigned to the students are doubles.
3. Which one of the following must be true?
(A) Lee is assigned to a single (B) Pat sharts a double with another student (C) Robin shares a double with another student (D) Two of the second-year students share a double with each other (E) Neither of the third-year students is assigned to a single
4. If Robin is assigred to a triple, which one of the following must be true?
(A) Lee is assigned to a single (B) Two second-year students share a double with each other (C) None of the rooms assigned to the students is a single (D) Two of the rooms assigned to the students are singles. (E) Three of the rooms assigned to the students are singles
5. If Terry and Val assigned to different doubles from each other, other, then it must be true of the students’ rooms that exactly
(A) one is a single (B) two are singles (C) two are doubles (D) one is a triple (E) two are triples
6. Which one of the following could be true?
(A) The two fourth-year students are assigned to singles. (B) The two fourth-year students share a double with cach other. (C) Lee shares a room with a second-year student (D) Lee shares a room with a third-year student (E) Pat shares a triple with two other students
Questions 7-11
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Seiection of bulbs for the sockets is governed by the following conditions:
Whenever light 1 is purple, light 2 must be yellow.
Whenever light 2 is purple, light 1 must be green.
Whenever light 3 is either purple or yellow, light 2 must be purple.
7. Which one of the following could be an accurate list of the colors of light bulbs 0selected for lights 1, 2 and 3, respectively?
(A) green, green, yellow (B) purple, green, green (C) purple, purple, green (D) yellow, purple, green (E) yellow, yellow, yellow
8. If light 1 is yellow, then any of the following can be true, EXCEPT:
(A) Light 2 is green. (B) Light 2 is purple (C) Light 3 is green (D) Light 3 is purple (E) Light 3 is yellow
9. There is exactly one possible color sequence of the three lights if which one of the following is true?
(A) Light 1 is purple. (B) Light 2 is purple. (C) Light 2 is yellow (D) Light 3 is purple. (E) Light 3 is yellow
10. If no green bulbs are 0selected, there are exactly how many possible different color sequences of the three lights?
(A) one (B) two (C) three (D) four (E) five
11. If no two lights are assigned light bulbs that are the same color as each other, then which one of the following could be true?
(A) Light I is green, and light 2 is purple. (B) Light I is green, and light 2 is yellow. (C) Light I is purple, and light 2 is yellow. (D) Light I is yellow, and light 2 is green. (E) Light I is yellow, and light 2 is purple.