Question 12-17
Six people-Julio, Kevin, May, Norma, Olivia, and Tamio-participate in a track meet. Two of them enter the marathon, two enter the relay, and two enter the sprint.
Each participant enters only one event.
If Kevin enters the marathon, then both Julio and
May enter the relay, and if both Julio and May enter the relay, then Kevin enters the marathon.
If Norma does not enter the sprint, then Tamio enters the relay.
If Olivia enters the relay, then Julio does not enter the relay.
Olivia and Tamio do not both enter the relay.
12. If Kevin enters the marathon, then which one of the following cannot be true?
(A) Julio enters the relay and Norma enters the sprint.
(B) Olivia enters the marathon and Norma enters the sprint.
(C) Tamio enters the marathon and Olivia enters the sprint.
(D) Tamio enters the relay and Olivia enters the sprint.
(E) Tamio enters the marathon and May enters the sprint.
13. If Norma enters the marathon, then which one of the following cannot be true?
(A) Both Kevin and Olivia enter the sprint.
(B) Kevin enters the relay and Olivia enters the sprint.
(C) Kevin enters the marathon and May enters the relay.
(D) Julio enters the marathon and May enters the relay.
(E) Julio enters the marathon and Kevin enters the relay.
14. If both Kevin and Olivia enter the relay, then which one of the following must be true?
(A) Julion and Tamio enter the marathon.
(B) May enters the marathon.
(C) May enters the sprint.
(D) Tamio enters the sprint.
(E) Norma enters the sprint.
15. If both Julio and Kevin enter the same event, then which of the following can be true?
Ⅰ.Julio enters the relay.
Ⅱ. May enters the marathon.
Ⅲ. Olivia enters the relay.
(A) Ⅰonly
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰand Ⅱonly
(E) Ⅰ,Ⅱ,and Ⅲ
16. If Norma and Olivia each enter different events, then which one of the following cannot be true?
(A) Kevin and Olivia enter the marathon.
(B) Julio and Norma enter the relay.
(C) May and Olivia enter the relay.
(D) Norma and Tamio enter the relay.
(E) Olivia enters the sprint and Tamio enters the relay.
17. If both Julio and Kevin enter the relay, then which one of the following must be false?
(A) May and Norma enter the marathon.
(B) May and Olivia enter the marathon.
(C) Norma and Tamio enter the sprint.
(D) May and Norma enter the sprint.
(E) May enters the sprint and Tamio enters marathon.
Questions 18-23
Seven lights-J, K, L, M, N, O, and P-have only two possible settings: on or off. They are arranged on a particular electric circuit as follows.
If K is on, L is off; if K is off, L is on.
J and N cannot both be on.
If M is off, either J or N is on; if either J or N is on, M is off.
If P is on, L is on.
If O is off, N is off; if O is on, N is on.
Assume that the circuit is working as designed.
18. Any of the following can be true EXCEPT:
(A) J and O are both off.
(B) K and N are both off.
(C) K and P are both on.
(D) L and M are both on.
(E) N and O are both on.
19. If L and O are on, which one of the following must be true?
(A) J is and K is off.
(B) J is off and N is on.
(C) K is off and M is on.
(D) K is off and P is on.
(E) M is off and P is on.
20. Which one of the following can be true?
(A) Only J, K, and M are off.
(B) Only J, L, and M are off.
(C) Only K, M, and O are off.
(D) Only L, N, and O are off.
(E) Only M, N, and O are off.
21. If P is on, what is the maximum number of lights that can be off?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
22. What is the minimum number of lights that must be on?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
23. If J is on, which one of the following could be a complete and accurate list of the remaining lights that are also on?
(A) K, L, and M
(B) L, N, and P
(C) L, O, and P
(D) M, N, and O
(E) L and P
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