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Time-35 minutes
23 Questions
Questoins 1-6
A man buys three outfits-X, Y, and Z-each of which consists of two articles
of clothing.
Each of the articles of clothing is either brown gray or navy.
At least one of the outfits is made up of two articles different in color
from one another.
No more than two of the outfits contain the same combination of colors.
Outfit X contains at least one navy article of clothing.
Outfit X contains at least one brown article of clothing and does not
contain a gray article.
1. Which one of the following can be the colors of the man’s outfits?
(A) X: gray and navy; Y: brown and gray; Z: gray and gray
(B) X: brown and gray; Y: brown and navy; Z: gray and gray
(C) X: navy and navy; Y: brown and brown; Z: brown and navy
(D) X: brown and navy; Y: brown and navy; Z: brown and navy
(E) X: navy and navy; Y: brown and brown; Z: navy and navy
2. If outfits X and Y each consist of one brown article and one navy article
of clothing, what combinations for outfit Z?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
3. If outfit Z does not contain two brown items of clothing, what is the
maximum number of items of clothing in the three outfits that can be navy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
4. If outfit Y consists of two brown articles of clothing and outfit Z consists
of two navy items, what is the total number of possible color combinations for
outfit X?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
5. Which one of the following color combinations for outfit Z would be
acceptable under any of the acceptable color combinations for outfits X and Y?
(A) gray and gray
(B) brown and gray
(C) brown and brown
(D) brown and navy
(E) navy and navy
6. If no two outfits contain the same color combination but each contains at
least one navy item, which one of the following is a complete and accurate
list of the possible combinations for outfit X?
(A) gray and navy
(B) brown and navy
(C) navy and navy
(D) gray and navy; brown and navy
(E) gray and navy; navy and navy
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Question 7-11
Five seats on a train are arranged in two rows that face each other. The
seats in row 1 are seat 1 and seat 2. The s
eats in row 2 are seat 3, seat 4,
and seat 5 in that order. Seat 1 is directly across from seat 3. Seat 2 is
directly across from seat 4. Seat 5 is not directly across from any other seat.
Three women-, Betty, and Carol-and two men-David Edmund-each must be seated in
one of me five seats, one person to a seat.
Betty sits in seat 4.
Carol sits next to neither Betty nor David.
Alice does not sit directly across from Carol.
7. If Edmund sits directly across from Betty, which one of the following must
be true?
(A) Alice does not sit directly across from anyone.
(B) Alice sits directly across from David.
(C) Alice sits next to Edmund.
(D) David sits next to Alice.
(E) David sits next to Edmund.
8. If Edmund does not sit directly across from anyone, which one of the
following is a complete and accurate list of those (other than Edmund) who
cannot sit in seat 1?
(A) Betty
(B) Carol
(C) David
(D) Betty and Carol
(E) Betty and David
9. If none of the five passengers sits directly across from a passenger of the
same sex, how many seating arrangements of the five passengers are possible?
(A) exactly 0
(B) exactly 1
(C) exactly 2
(D) exactly 3
(E) exactly 4
10. How many of the seats could be the one Alice selects as her seat?
(A) 1 only
(B) 2 only
(C) 3 only
(D) 4 only
(E) 5 only
11. How many different seating arrangements of the passengers might there be
for row 2?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
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) T
amio 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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