GAT-B Arts, Humanities and Social Science Analytical Online Test Preparation for Pakistani Students

Question # 1

Five ladies, Ayesha, Bano, Chandni, Durya, and Elina enter in a series of baking contests in which they are to place their Biryani dish to the judges. The series follows the rules of presentation given below: Bano places ahead of Chandni. Either Ayesha is first and Elina is last, or Elina is first and Ayesha is last. There are no ties in any contest. Everyone competes in each contest.
Q:If exactly one lady places between Ayesha and Bano, which of the following must be true?

Ayesha wins first place A
Elina wins first place B
Durya places third C
Bano places fourth D
Chandni places fourth E

Question # 2

Multan Institute of Higher Studies plans to show five educational films A, B, C, D, and E to a group of students. The film shows are planned in an order, which conforms to the following conditions:
A must be shown earlier than C.
B must be shown earlier than D.
E should be the fifth film shown.
Q:In case D and E are shown as far apart from each other as possible, which among the following would be true?

A is shown earlier than B A
B is shown earlier than C B
C is shown earlier than E C
D is shown earlier than A D
E is shown earlier than B E

Question # 3

On a factory control room, there are three ON-OFF switches on central control panel, labeled A,B, and C. They are changed from default setting to a required setting based on the following rules:
In case only switch A is ON in the default setting, then turn switch BON..
In case switches A and B are the only switches ON in the default setting, then turn switch CON. In case all the three switches are ON,in default setting, then turn the switch C OFF. For any other default setting turn ON all switches that are OFF and turn OFF all switches,if any, that are ON.
Q:In case only switch B is ON in the default setting, what must be the second setting?

AON,BON,CON A
AON,BON,COFF B
AOFF,BOFF,CON C
AOFF,BOFF,COFF D
AOFF,BOFF,COFF E

Question # 4

Many people do not read the books they purchase.For example seventeen percent of college students in Pakistan have textbooks,but only forty-five percent of them read more than once a year and only seventeen percent read more than once a week.Q-Which of the following if true costs doubt on the claim that most people read the books they purchase?

Readers often exaggerate about their book reading. A
The sale of novels is more than that of other types. B
Many people buy books to pretend themselves as a scholar. C
Regular book readers are most susceptible to eye diseases. D
Reading speed is increased by frequent readings. E

Question # 5

In a shopping mall, six steps lead from the first to the second floor. Four peoples A, B, C, and D are to go from first floor to the second floor following the rules given below. No two people can be on the same step. A is two steps below C. B is a step next to D. Only one-step is vacant (No one standing on that step). Denote the first step by step I and second step by step 2 etc.
Q: If E was on the third step and B was on a higher step than E which step must be vacant

step 1 A
step 2 B
step 4 C
step 5 D
step 6 E

Question # 6

A city map representing roads M,N,O,P,Q and R.Link roads cannot have the same colour in the map.The roads link to each other are as under:Each M,N,P and Q has link to O.P has a link to Q.Each of M and N has a link to R.Which of the following roads can be the same colour as O on the map?

N A
P B
Q C
R D

Question # 7

An island, five kilometers away in the sea is connected to the land by two ways, three hanging bridges A, B, and C and three water routes 1,2 and 3.The managing authority offers services to people for coming in and for going out by officially managed vehicles on both ways. When it snows, morning service on B is delayed. When it rains or snows, service on A, route 2 and route 3 are delayed in both the morning and afternoon When temperature falls below 30 degrees Fahrenheit afternoon service is cancelled on either A or on the route 3, but not both.When the temperature rises over 90 degrees Fahrenheit, the afternoon service is cancelled in either on C or on the route 3 but not both.When the service on A is delayed or cancelled, service on the C, which connects A is delayed.When service on the router 3 is cancelled, service on B, which connects the route 3 is delayed.
Q:On which of the following occasions would maximum number of services be disrupted

A snowy afternoon with the temperature at 45 degree Fahrenheit A
A snowy morning with the temperature at 45 degree Fahrenheit B
A rainy afternoon with the temperature at 45 degree Fahrenheit C
A rainy afternoon with the temperature at 95 degree Fahrenheit D

Question # 8

The principal of a college is forming a committee.There are to be five members:three teachers,chosen from Mr A,Mr C, Mr.D, Mr E; and two students,chosen from L,M,N and O. The composition of the committee must conform the following conditions:Q-In how many different ways can the principal select an acceptable committee?

Less than 3 A
3 B
7 C
More than 7 D
5 E

Question # 9

Nine individuals - Z, Y, X, W, V, U, T, S and R are to serve on three committees labeled A, B and C. Each candidate should serve on exactly one of the committees. Committee A should consist of exactly one member more than that of committee B. It is possible that there are no members of committee C Among Z, Y and X none can serve on committee A. Among W, V and U none can serve on committee C. Among T, S and R none can serve on committee C.
Q:In case T, S and X are the only individuals serving on committee B, the total membership of committee C should be:

Z and Y A
Z and W B
Y and V C
Y and U D
X and V E

Question # 10

During practice matches,before a major tournament,in a football ground,one team can practice at a time.There are seven teams-- the Argentine,the Brazil the Senegal,the Dubai,the England,the France and the Germany,The football ground is open seven evenings a week from Monday to Sunday (Sunday being considered the last day of the week),and the allocation of the practice times is governed by the following rules:i.On any evening only one team can play.ii.The Argentine must practice on Monday.iii.The Dubai practice exactly one day before the France practice.iv,The France practice exactly one day before the Germany practice.v.The Senegal and the Brazil must practice earlier in the week than the England.Q-If the Germany practice on Thursday,the England and the Dubai must practice on which days,respectively?

Sunday and Tuesday A
Saturday and Tuesday B
Friday and Wednesday C
Wednesday and Thursday D
Tuesday and Monday E

Question # 11

The primary evil of today's society is selfishness.People are concerned only with themselves.Personal advancement is the sole motivating force in our world.This is not to say that individuals are never willing to help one another,on the contrary,.............However,these are only short-term occurrences which ultimately serve our long-term goal of personal gain.Q-Which statement would most strongly contradict the author's attitude towards society?

Altruism is society's greatest strength. A
The forces of good will ultimately triumph over evil. B
Our short-term actions may ostensibly contradict our long-term goals C
We must all learn the art of selfishness. D
Morality is the bedrock of a growing community. E

Question # 12

Four captains and the first mates of three of them were to attend the annual meeting at head quarters. The captains were Luqman, Manzoor, Nauman, and Osaf, the mates were Ayesha, Durya, and Gia. Each person in turn delivered a report to the chairperson as follows: Each of the first mates delivered their report exactly after captain. The first captain to speak was Manzoor, and in Nauman spoke after him. . present the person with first letter of his name)
Q:In case A is the third of the first mates to speak, and L is the captain whose first mate is not present, which among the following statements must be true?

A spoke sometime before L A
D spoke sometime before O B
L spoke sometime before O C
O spoke sometime before L D
O spoke sometimes before N E

Question # 13

Three women--X,Y, and Z are traveling in a van with five children--A,B,C,D and E The van has a driver's seat and one passenger seat in the front and two benches behind the front seats, one bench behind the first.Each bench has room for exactly three people.Every one must sit in a seat or on a bench and seating is subject to the following restrictions: A women must sit on each bench.Either X or Y must sit in the driver's seat.C must sit immediately beside E.Q-Which of the following can sit in the front passenger seat?

C A
D B
X C
Y D
Z E

Question # 14

In a city, police commissioner planed to educate the citizens the traffic rules. He arranged a separate department and appointed senior staff members as instructors. Students in this class are required to meet the chief instructor once per term. The chief instructor offers meeting times on one day, one meeting time in the morning, one in the afternoon, and one in the evening. The students in the class this term are Farid, Gia, Hamid, Javed, Kamran, Lubna, Majeed, and Nargis. The meetings with the chief instructor must conform to the following conditions: The chief instructor will not meet with only one student at a time. The chief instructor must meet with at least one student in each of the available meeting times. ',arid and Javed cannot attend the same meeting. Kamran and Majced cannot attend the same meeting. If Gia attends the morning meeting, then Kamran must attend the evening meeting. If Javed attends the afternoon meeting, then Hamid must attend the afternoon meeting. The number of students who meet in the morning must be the same as the number of students who meet in the evening.
Q:If Gia and Lubna are the only students who meet in the morning, then which of the following CANNOT be true?

Farid meets in the evening A
Hamid meets in the afternoon B
Javed meets in the afternoon C
Nargis meets in the evening D
Majeed meets in the afternoon E

Question # 15

A Government College sports president wishes to select four members of a sports-wing committee as special representatives to meet the requirements of college's sports activities.The committee consists of eight members four of which (K,L,M and M) are sports teachers whereas the other four (P,Q,R andS) are students.The four representatives must consist of exactly two sports teachers and two students.Either K or L must be one of the representatives but K and L both cannot be the representatives.If P is a If R is a representative then L cannot be a representative.Q-If L is a representative then which of the following can be the other three representatives?

K,Q and S A
M,N and P B
M, P and Q C
N,p and S D

Question # 16

The customer complaint department of a chain of departmental stores firm employs exactly six people who answer letters: A,B,C,D,E and F.Every complaint letter received by the departmental is classified as either Red or Blue,The procedures for answering the letter are:Red letters are given first to A or B.Blue letters are given first to anyone of the following:A,D or C.If a letter raises a problem that cannot be resolved by the person to whom it is given,it must be forwarded until it reaches someone who can resolve the problem and answer the letter.A letter must be forwarded as follows:By A to C if the letter is Red,but to D if the letter is Blue;By B to either A to C;By C to D if the letter is Red,but to E if the letter is Blue;By D to either C or E whether the letter is Red or Blue;By E to F whether the letter is Red or Blue.F answer every letter given to him.Q-If a member of the consumer complaint department is given a letter that he or she had previously given to some other member of the department,the person who is given the letter a second time could be?

A A
B B
D C
E D
F E

Question # 17

Sales manager Nasir All is trying to establish a sales team to cover the Lahore region. His team will consist of four members - two experienced and two new sales representatives. Saleem, Fawad, Hanif, and Karim are the experienced sales representatives. Javed, Taimoor, and Daud arc new. Saleem and Fawad do not work together Taimoor and Saleem refuse to work.together. Hanif and Daud cannot work together.
Q: Which one of the following must be true?

Fawad and Saleem always work together A
Karim and Daud never work together B
Karim and Fawad always work together C
If Javed works, then Karim does't work D
If Saleem works, then Daud works E

Question # 18

Three women--X,Y, and Z are traveling in a van with five children--A,B,C,D and E The van has a driver's seat and one passenger seat in the front and two benches behind the front seats, one bench behind the first.Each bench has room for exactly three people.Every one must sit in a seat or on a bench and seating is subject to the following restrictions: A women must sit on each bench.Either X or Y must sit in the driver's seat.C must sit immediately beside E.Q-Which of the following groups of three can sit together on a bench?

A,C and E A
A.C and Z B
A.Y and Z C
B,D and Y D
D,E and X E

Question # 19

I All A's are B's
II All A's are C's or D's
III All C's and D's are A's
IV All E's are D's
V All G's are F's
VI No F's are A's
Q: If no P's are D's which of the following must be true

No P is an A A
No P is an B B
If any P is an B it is an A C
If any P is an A it is a C D

Question # 20

An Internal Services Manager at a large corporation has been assigned the task of allotting offices to six of the staff members. The offices are titled AthroughF. Mrs. Ruby needs to use the telephone quite often throughout the day. Mr. Mujahid and Mr. Zahid need adjacent offices as they need to consult each other often while working. Mrs. Fauzia is a senior employee and has to be allotted the office markedE, having the biggest window. Mr. Abid requires silence in the offices next to his Mr. Shahid, Mr. Mujahid, and Mr. Abid are all smokers. Mrs.Fauziarequires non-smoker neighbors. Unless specifically stated all the employees maintain an atmosphere of silence during office hours.
Q: The ideal candidate to occupy the office farthest from Mr.Zahid would be

Mrs.Fauzia A
Mr.Mujahid B
Mr.Shahid C
Mr.Abid D

Question # 21

Two or more tealeaves out of five varieties-- Livana, Mathia, Novajana, Oxia, and Piask are used in making all branded blends by a marketer following the rules given below. A brand containing Livana should also contain Novajana twice that of Livana. A brand containing Mathia must also have equal quantity of Oxia. A single brand never contains Novajana as well as Oxia. Oxia and Piask should not be used together. A blend containing Piask should contain it in such a proportion that the total amount of Piask present should be greater than the total amount of the other tea leaves.
Q:Among the following which is an acceptable brand in accordance with the rules?

One part Livana, one part Piask A
Two parts Mathia, two parts Livana B
Three parts Novajana, three parts Livana C
Four parts Oxia, four parts Mathia D

Question # 22

Three women--X,Y, and Z are traveling in a van with five children--A,B,C,D and E The van has a driver's seat and one passenger seat in the front and two benches behind the front seats, one bench behind the first.Each bench has room for exactly three people.Every one must sit in a seat or on a bench and seating is subject to the following restrictions: A women must sit on each bench.Either X or Y must sit in the driver's seat.C must sit immediately beside E.Q-If A sits immediately beside Z,which of the following CANNOT be true?

C sits immediately beside Y. A
D sits immediately beside Z. B
B sits in the front passenger seat. C
A sits on the same bench as B D
B sits on the same bench as X E

Question # 23

An island, five kilometers away in the sea is connected to the land by two ways, three hanging bridges A, B, and C and three water routes 1,2 and 3.The managing authority offers services to people for coming in and for going out by officially managed vehicles on both ways. When it snows, morning service on B is delayed. When it rains or snows, service on A, route 2 and route 3 are delayed in both the morning and afternoon When temperature falls below 30 degrees Fahrenheit afternoon service is cancelled on either A or on the route 3, but not both.When the temperature rises over 90 degrees Fahrenheit, the afternoon service is cancelled in either on C or on the route 3 but not both.When the service on A is delayed or cancelled, service on the C, which connects A is delayed.When service on the router 3 is cancelled, service on B, which connects the route 3 is delayed.
Q: On August 15th with the temperature at 97 degrees Fahrenheit, it begin to rain at 1 PM. What is the minimum number of services will be affected?

2 A
3 B
4 C
5 D

Question # 24

Multan Institute of Higher Studies plans to show five educational films A, B, C, D, and E to a group of students. The film shows are planned in an order, which conforms to the following conditions:
A must be shown earlier than C.
B must be shown earlier than D.
E should be the fifth film shown.
Q:In case, C is shown earlier than E, which among the following will hold true?

A is the second film shown A
B is the second film shown B
C is the third film shown C
D is the fourth film shown D
E is the fourth film shown E

Question # 25

According to Albert Einstein's famous theory of relativity,time travel is theoretically possible,If we assume that time travel were to be possible through some technological wonder,it would be advantageous to send someone back in time to prevent the assassination of Archduke Franz Ferdinand in 1914 and thus keep Word War I from ever occurring.Q-The argument above makes which of the following assumptions?

The technology necessary for time travel is likely to be developed in the near future. A
If the time travel were to be developed in the future,evidence of time travelers would be apparent to those living today. B
It is not possible to alter a significant current in world history merely by changing a single event. C
If Franz Ferdinand had not been assassinated,some other catalytic event would have led to the start of World War I. D
The assassination of Franz Ferdinand was the crucial event that triggered the start of Word War I. E

Question # 26

Four captains and the first mates of three of them were to attend the annual meeting at head quarters. The captains were Luqman, Manzoor, Nauman, and Osaf, the mates were Ayesha, Durya, and Gia. Each person in turn delivered a report to the chairperson as follows: Each of the first mates delivered their report exactly after captain. The first captain to speak was Manzoor, and in Nauman spoke after him. . present the person with first letter of his name)
Q: In Case A spoke immediately after L and immediately before O, and O was not the last speaker Lspoke

second A
third B
fourth C
sixth D

Question # 27

The office staff of a firm engaged in marketing of innovative gimmicks consists of three accountants--A, B, C and five secretaries-- D, E, F, G, H. The top management is planning to expand its market by opening a new setup in another city using two accountants and three secretaries of the present staff. To do so they plan to separate certain individuals who don't function well together. The following guidelines were established to set up the new office
I Accountants A and C cannot work together happily as A is a chain smoker and C is allergic to smoking and should not be sent together to the new office as a team
II C and E function well alone but quarrel when work together so, they should be sent to the new office as a team
Ill D and G have not been on speaking terms and shouldn't go together
IV Since D and F have been competing for promotion they shouldn't be a team.
Q: If C is switched to the new office, which of the following cannot move to the new office

B A
D B
F C
G D

Question # 28

The office staff of a firm engaged in marketing of innovative gimmicks consists of three accountants--A, B, C and five secretaries-- D, E, F, G, H. The top management is planning to expand its market by opening a new setup in another city using two accountants and three secretaries of the present staff. To do so they plan to separate certain individuals who don't function well together. The following guidelines were established to set up the new office
I Accountants A and C cannot work together happily as A is a chain smoker and C is allergic to smoking and should not be sent together to the new office as a team
II C and E function well alone but quarrel when work together so, they should be sent to the new office as a team
Ill D and G have not been on speaking terms and shouldn't go together
IV Since D and F have been competing for promotion they shouldn't be a team.
Q: Which of the following must switched to the new office

B A
D B
E C
G D

Question # 29

Two statements,labeled (1) and (2),follow each of the following given questions.The statements contain certain information in the question you do not actually have to compute an answer,rather than you have to decide whether the information given in the statements (1) and (2) is sufficient to find a correct answer by using basic mathematics and everyday fact?Q-Can any of the four rivers be more than 200 meters wide?1.The narrowest of the four rivers is 140 meters wide.2.Average width of the four rivers is 200 meters.

Statement 1.Alone is sufficient but 2. ALONE is not sufficient to answer this question. A
Statement 2.ALONE is sufficient but 1.ALONE is not sufficient to answer this question. B
Statements 1 and 2.TOGETHER are sufficient to answer the question but NEITHER of them is sufficient ALONE. C
Statements 1 and 2 COMBINED are not sufficient to answer the question and additional information is needed to find the correct answer. D

Question # 30

A Government College sports president wishes to select four members of a sports-wing committee as special representatives to meet the requirements of college's sports activities.The committee consists of eight members four of which (K,L,M and M) are sports teachers whereas the other four (P,Q,R andS) are students.The four representatives must consist of exactly two sports teachers and two students.Either K or L must be one of the representatives but K and L both cannot be the representatives.If P is a If R is a representative then L cannot be a representative.Q-If P is a representative then which of the following CANNOT be a representative?

M A
N B
Q C
R D

Sr.#	Question	Answer
1	The principal of a college is forming a committee.There are to be five members:three teachers,chosen from Mr A,Mr C, Mr.D, Mr E; and two students,chosen from L,M,N and O. The composition of the committee must conform the following conditions:Q-How many different committee could include Mr A and N?	A. 1 B. 2 C. 3 D. 4
2	The accounts staff of the Mark corporation presently consists of three book-keepers (X,Y and Z) and five Data Entry Operators (M,N,O,P and Q) Management is planning to open a new office in another city sending three Data Entry Operators and two book-keepers from the present staff.To do so they plan to separate certain individuals who do not function well together.The following guidelines were established to set up the new office:(i) Book-keepers X and Z are constantly finding faults with one another therefore should not be sent together to the new office.(ii) Z and N function well alone but not as a team.They should be separated.(iii) M and P have not been on speaking terms for many months they should not go together.(iv) Since M and O have been competing for a promotion they should not be in one team.Based on the above information find the correct answers to the following questions:Q-If X is to be moved as one of the book-keepers,which of the following CANNOT be a possible working unit?	A. X Y M N Q B. X Y N O Q C. X Y M P Q D. X Y N P Q
3	The office staff of a firm engaged in marketing of innovative gimmicks consists of three accountants--A, B, C and five secretaries-- D, E, F, G, H. The top management is planning to expand its market by opening a new setup in another city using two accountants and three secretaries of the present staff. To do so they plan to separate certain individuals who don't function well together. The following guidelines were established to set up the new office I Accountants A and C cannot work together happily as A is a chain smoker and C is allergic to smoking and should not be sent together to the new office as a team II C and E function well alone but quarrel when work together so, they should be sent to the new office as a team Ill D and G have not been on speaking terms and shouldn't go together IV Since D and F have been competing for promotion they shouldn't be a team. Q: If D goes to the new office, which of the following is/are true I C cannot go II A cannot go III H must also go	A. I only B. I and II only C. II only D. I and III only
4	An Internal Services Manager at a large corporation has been assigned the task of allotting offices to six of the staff members. The offices are titled AthroughF. Mrs. Ruby needs to use the telephone quite often throughout the day. Mr. Mujahid and Mr. Zahid need adjacent offices as they need to consult each other often while working. Mrs. Fauzia is a senior employee and has to be allotted the office markedE, having the biggest window. Mr. Abid requires silence in the offices next to his Mr. Shahid, Mr. Mujahid, and Mr. Abid are all smokers. Mrs.Fauziarequires non-smoker neighbors. Unless specifically stated all the employees maintain an atmosphere of silence during office hours. Q: The ideal office for Mr.Mujahid would be	A. B B. F C. A D. C
5	Four captains and the first mates of three of them were to attend the annual meeting at head quarters. The captains were Luqman, Manzoor, Nauman, and Osaf, the mates were Ayesha, Durya, and Gia. Each person in turn delivered a report to the chairperson as follows: Each of the first mates delivered their report exactly after captain. The first captain to speak was Manzoor, and in Nauman spoke after him. . present the person with first letter of his name) Q: In Case A spoke immediately after L and immediately before O, and O was not the last speaker Lspoke	A. second B. third C. fourth D. sixth
6	A Government College sports president wishes to select four members of a sports-wing committee as special representatives to meet the requirements of college's sports activities.The committee consists of eight members four of which (K,L,M and M) are sports teachers whereas the other four (P,Q,R andS) are students.The four representatives must consist of exactly two sports teachers and two students.Either K or L must be one of the representatives but K and L both cannot be the representatives.If P is a If R is a representative then L cannot be a representative.Q-If P is a representative then which of the following CANNOT be a representative?	A. M B. N C. Q D. R
7	A researcher has concluded that woman are just as capable as men in math but that their skills are not developed because society expects them to develop other and more diverse abilities.Q.Which of the following is a basic assumption of the researcher?	A. Ability in math is more important than ability is more divers subjects. B. Ability in math is less important than ability in more divers subjects. C. Women and men should be equally capable in math. D. Women might be more capable than men in math.
8	Many people do not read the books they purchase.For example seventeen percent of college students in Pakistan have textbooks,but only forty-five percent of them read more than once a year and only seventeen percent read more than once a week.Q-Which of the following if true costs doubt on the claim that most people read the books they purchase?	A. Readers often exaggerate about their book reading. B. The sale of novels is more than that of other types. C. Many people buy books to pretend themselves as a scholar. D. Regular book readers are most susceptible to eye diseases.
9	A home furniture dealer has seven laxury sofas in his showroom: a Z, a Y, a X, a W, a V, a U and a T. The dealer must.place the sofas in one of seven showroom spaces that are numbered 1-7 from left to right. Each showroom space must be filled with exactly one sofa. The following conditions apply to the placement of the sofas in the showroom: 1 X must not be placed in a space adjacent to W. 2 Z must be placed in a space adjacent to T. 3 Y must be placed in the first or the last space. 11V is placed in the third space, then W must be placed in the fifth space Q:Which of the following is an acceptable placement of the sofas in the showroom spaces from one to seven?	A. Z, T, V, X, W, U, Y B. Y, X, V, U, W, Z, T C. X, Y, U, W, T, Z, V D. Y, Z, V, U, W, T, X
10	On a factory control room, there are three ON-OFF switches on central control panel, labeled A,B, and C. They are changed from default setting to a required setting based on the following rules: In case only switch A is ON in the default setting, then turn switch BON.. In case switches A and B are the only switches ON in the default setting, then turn switch CON. In case all the three switches are ON,in default setting, then turn the switch C OFF. For any other default setting turn ON all switches that are OFF and turn OFF all switches,if any, that are ON. Q:In case only switch B is ON in the default setting, what must be the second setting?	A. AON,BON,CON B. AON,BON,COFF C. AOFF,BOFF,CON D. AOFF,BOFF,COFF

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GAT-B Arts, Humanities & Social Science Analytical

A city map representing roads M,N,O,P,Q and R.Link roads cannot have the same colour in the map.The roads link to each other are as under:Each M,N,P and Q has link to O.P has a link to Q.Each of M and N has a link to R.Which of the following roads can be the same colour as O on the map?

I All A's are B'sII All A's are C's or D'sIII All C's and D's are A'sIV All E's are D'sV All G's are F'sVI No F's are A'sQ: If no P's are D's which of the following must be true

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I All A's are B's
II All A's are C's or D's
III All C's and D's are A's
IV All E's are D's
V All G's are F's
VI No F's are A's
Q: If no P's are D's which of the following must be true