Analytical Reasoning Aptitude MCQ Questions with Answers Set 01

Arithmetic Ability Objective Questions and Answers: Analytical Reasoning

Explore reliable objective questions for Analytical Reasoning tailored for General Aptitude learners. Utilizing these Arithmetic Ability multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

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Multiple Choice Questions

Question 1: Directions: A, B, C, D and E are five friends who stay in Sea View Apartments in Mumbai. They are a Doctor, an Advocate, a Banker, an Engineer and an Auditor, but not in the same order. Each plays a different game.
(1) A plays Cricket but is not an Engineer.
(2) D, who is an Auditor, does not play Hockey.
(3) The Advocate and the Doctor are not interested in Basketball.
(4) B is an expert Golf player but is not an Advocate.
(5) E finds time on Sunday morning to play Tennis and he is a Banker.
(6) C, who does not like Golf, is neither a Doctor nor an Advocate.
(7) The Engineer is always the centre forward in Hockey.

Who is a basketball player?
(a) A
(b) C
(c) D
(d) B
Show Answer & Explanation

Answer: (c) D

Explanation:
1. Games fixed directly: A - Cricket, B - Golf, E - Tennis. Professions fixed: D - Auditor, E - Banker.
2. C and D share Hockey and Basketball; D does not play Hockey, so D plays Basketball and C plays Hockey.
3. The Engineer plays Hockey, so C is the Engineer. A and B are left with Doctor and Advocate; B is not an Advocate, so B is the Doctor and A is the Advocate.
4. So the Basketball player is D, the Auditor.

Teacher's Note:
1. Build a grid of persons against professions and games, and mark every direct fact first before making deductions.
2. When only two persons are left for two slots, one negative clue is enough to fix both of them.

Question 2: Directions: A, B, C, D and E are five friends who stay in Sea View Apartments in Mumbai. They are a Doctor, an Advocate, a Banker, an Engineer and an Auditor, but not in the same order. Each plays a different game.
(1) A plays Cricket but is not an Engineer.
(2) D, who is an Auditor, does not play Hockey.
(3) The Advocate and the Doctor are not interested in Basketball.
(4) B is an expert Golf player but is not an Advocate.
(5) E finds time on Sunday morning to play Tennis and he is a Banker.
(6) C, who does not like Golf, is neither a Doctor nor an Advocate.
(7) The Engineer is always the centre forward in Hockey.

Who is a doctor?
(a) B
(b) D
(c) A
(d) E
Show Answer & Explanation

Answer: (a) B

Explanation:
1. Games fixed directly: A - Cricket, B - Golf, E - Tennis. Professions fixed: D - Auditor, E - Banker.
2. C and D share Hockey and Basketball; D does not play Hockey, so D plays Basketball and C plays Hockey.
3. The Engineer plays Hockey, so C is the Engineer. A and B are left with Doctor and Advocate; B is not an Advocate, so B is the Doctor and A is the Advocate.
4. Therefore the Doctor is B.

Teacher's Note:
1. Build a grid of persons against professions and games, and mark every direct fact first before making deductions.
2. When only two persons are left for two slots, one negative clue is enough to fix both of them.

Question 3: Directions: A, B, C, D and E are five friends who stay in Sea View Apartments in Mumbai. They are a Doctor, an Advocate, a Banker, an Engineer and an Auditor, but not in the same order. Each plays a different game.
(1) A plays Cricket but is not an Engineer.
(2) D, who is an Auditor, does not play Hockey.
(3) The Advocate and the Doctor are not interested in Basketball.
(4) B is an expert Golf player but is not an Advocate.
(5) E finds time on Sunday morning to play Tennis and he is a Banker.
(6) C, who does not like Golf, is neither a Doctor nor an Advocate.
(7) The Engineer is always the centre forward in Hockey.

What is the profession of A?
(a) Doctor
(b) Advocate
(c) Banker
(d) Auditor
Show Answer & Explanation

Answer: (b) Advocate

Explanation:
1. Games fixed directly: A - Cricket, B - Golf, E - Tennis. Professions fixed: D - Auditor, E - Banker.
2. C and D share Hockey and Basketball; D does not play Hockey, so D plays Basketball and C plays Hockey.
3. The Engineer plays Hockey, so C is the Engineer. A and B are left with Doctor and Advocate; B is not an Advocate, so B is the Doctor and A is the Advocate.
4. Therefore A is the Advocate.

Teacher's Note:
1. Build a grid of persons against professions and games, and mark every direct fact first before making deductions.
2. When only two persons are left for two slots, one negative clue is enough to fix both of them.

Question 4: Directions: A, B, C, D and E are five friends who stay in Sea View Apartments in Mumbai. They are a Doctor, an Advocate, a Banker, an Engineer and an Auditor, but not in the same order. Each plays a different game.
(1) A plays Cricket but is not an Engineer.
(2) D, who is an Auditor, does not play Hockey.
(3) The Advocate and the Doctor are not interested in Basketball.
(4) B is an expert Golf player but is not an Advocate.
(5) E finds time on Sunday morning to play Tennis and he is a Banker.
(6) C, who does not like Golf, is neither a Doctor nor an Advocate.
(7) The Engineer is always the centre forward in Hockey.

Who plays hockey?
(a) B
(b) A
(c) E
(d) C
Show Answer & Explanation

Answer: (d) C

Explanation:
1. Games fixed directly: A - Cricket, B - Golf, E - Tennis. Professions fixed: D - Auditor, E - Banker.
2. C and D share Hockey and Basketball; D does not play Hockey, so D plays Basketball and C plays Hockey.
3. The Engineer plays Hockey, so C is the Engineer. A and B are left with Doctor and Advocate; B is not an Advocate, so B is the Doctor and A is the Advocate.
4. Therefore C plays Hockey.

Teacher's Note:
1. Build a grid of persons against professions and games, and mark every direct fact first before making deductions.
2. When only two persons are left for two slots, one negative clue is enough to fix both of them.

Question 5: Directions: A, B, C, D and E are five friends who stay in Sea View Apartments in Mumbai. They are a Doctor, an Advocate, a Banker, an Engineer and an Auditor, but not in the same order. Each plays a different game.
(1) A plays Cricket but is not an Engineer.
(2) D, who is an Auditor, does not play Hockey.
(3) The Advocate and the Doctor are not interested in Basketball.
(4) B is an expert Golf player but is not an Advocate.
(5) E finds time on Sunday morning to play Tennis and he is a Banker.
(6) C, who does not like Golf, is neither a Doctor nor an Advocate.
(7) The Engineer is always the centre forward in Hockey.

What is the profession of C?
(a) Banker
(b) Auditor
(c) Engineer
(d) Advocate
Show Answer & Explanation

Answer: (c) Engineer

Explanation:
1. Games fixed directly: A - Cricket, B - Golf, E - Tennis. Professions fixed: D - Auditor, E - Banker.
2. C and D share Hockey and Basketball; D does not play Hockey, so D plays Basketball and C plays Hockey.
3. The Engineer plays Hockey, so C is the Engineer. A and B are left with Doctor and Advocate; B is not an Advocate, so B is the Doctor and A is the Advocate.
4. Therefore C is the Engineer.

Teacher's Note:
1. Build a grid of persons against professions and games, and mark every direct fact first before making deductions.
2. When only two persons are left for two slots, one negative clue is enough to fix both of them.

Question 6: Directions: Four men Venkat, Jayanth, Murali and Trilok are a sales executive, an accountant, a lawyer and a doctor by profession, but not in the same order. They are accompanied by their children to a magic show, and each person is with only one child. Trilok and Jayanth came with their sons and none of them is a sales executive or a doctor. Neetu, a sweet cute girl, is not the doctor's daughter. Gagan is not Jayanth's son. Sumanth's father is not an accountant. Teena is not Murali's daughter.

Who is the child of the sales executive?
(a) Neetu
(b) Gagan
(c) Sumanth
(d) Teena
Show Answer & Explanation

Answer: (a) Neetu

Explanation:
1. Trilok and Jayanth have sons (Gagan, Sumanth) and are the accountant and the lawyer; Venkat and Murali have daughters (Neetu, Teena) and are the sales executive and the doctor.
2. Gagan is not Jayanth's son, so Gagan is Trilok's son and Sumanth is Jayanth's. Sumanth's father is not the accountant, so Jayanth is the lawyer and Trilok the accountant.
3. Teena is not Murali's daughter, so Teena is Venkat's and Neetu is Murali's. Neetu is not the doctor's daughter, so Murali is the sales executive and Venkat the doctor.
4. The sales executive is Murali, whose child is Neetu.

Teacher's Note:
1. Split the people into groups first (fathers of sons vs fathers of daughters); it halves the possibilities at once.
2. Use each negative clue inside its small group, where a single 'not' immediately fixes the pairing.

Question 7: Directions: Four men Venkat, Jayanth, Murali and Trilok are a sales executive, an accountant, a lawyer and a doctor by profession, but not in the same order. They are accompanied by their children to a magic show, and each person is with only one child. Trilok and Jayanth came with their sons and none of them is a sales executive or a doctor. Neetu, a sweet cute girl, is not the doctor's daughter. Gagan is not Jayanth's son. Sumanth's father is not an accountant. Teena is not Murali's daughter.

Who is Gagan's father and what is he?
(a) Trilok - sales executive
(b) Venkat - sales executive
(c) Murali - accountant
(d) Trilok - accountant
Show Answer & Explanation

Answer: (d) Trilok - accountant

Explanation:
1. Trilok and Jayanth have sons (Gagan, Sumanth) and are the accountant and the lawyer; Venkat and Murali have daughters (Neetu, Teena) and are the sales executive and the doctor.
2. Gagan is not Jayanth's son, so Gagan is Trilok's son and Sumanth is Jayanth's. Sumanth's father is not the accountant, so Jayanth is the lawyer and Trilok the accountant.
3. Teena is not Murali's daughter, so Teena is Venkat's and Neetu is Murali's. Neetu is not the doctor's daughter, so Murali is the sales executive and Venkat the doctor.
4. So Gagan's father is Trilok, the accountant.

Teacher's Note:
1. Split the people into groups first (fathers of sons vs fathers of daughters); it halves the possibilities at once.
2. Use each negative clue inside its small group, where a single 'not' immediately fixes the pairing.

Question 8: Directions: Four men Venkat, Jayanth, Murali and Trilok are a sales executive, an accountant, a lawyer and a doctor by profession, but not in the same order. They are accompanied by their children to a magic show, and each person is with only one child. Trilok and Jayanth came with their sons and none of them is a sales executive or a doctor. Neetu, a sweet cute girl, is not the doctor's daughter. Gagan is not Jayanth's son. Sumanth's father is not an accountant. Teena is not Murali's daughter.

If Sumanth and Gagan are cousins, which two men are brothers?
(a) Venkat and Murali
(b) Venkat and Trilok
(c) Jayanth and Trilok
(d) Jayanth and Murali
Show Answer & Explanation

Answer: (c) Jayanth and Trilok

Explanation:
1. Trilok and Jayanth have sons (Gagan, Sumanth) and are the accountant and the lawyer; Venkat and Murali have daughters (Neetu, Teena) and are the sales executive and the doctor.
2. Gagan is not Jayanth's son, so Gagan is Trilok's son and Sumanth is Jayanth's. Sumanth's father is not the accountant, so Jayanth is the lawyer and Trilok the accountant.
3. Teena is not Murali's daughter, so Teena is Venkat's and Neetu is Murali's. Neetu is not the doctor's daughter, so Murali is the sales executive and Venkat the doctor.
4. Sumanth's father is Jayanth and Gagan's father is Trilok; if the boys are cousins, Jayanth and Trilok are brothers.

Teacher's Note:
1. Split the people into groups first (fathers of sons vs fathers of daughters); it halves the possibilities at once.
2. Use each negative clue inside its small group, where a single 'not' immediately fixes the pairing.

Question 9: Directions: Four men Venkat, Jayanth, Murali and Trilok are a sales executive, an accountant, a lawyer and a doctor by profession, but not in the same order. They are accompanied by their children to a magic show, and each person is with only one child. Trilok and Jayanth came with their sons and none of them is a sales executive or a doctor. Neetu, a sweet cute girl, is not the doctor's daughter. Gagan is not Jayanth's son. Sumanth's father is not an accountant. Teena is not Murali's daughter.

Who is Teena's father and what is his profession?
(a) Venkat - sales executive
(b) Trilok - accountant
(c) Jayanth - lawyer
(d) Venkat - doctor
Show Answer & Explanation

Answer: (d) Venkat - doctor

Explanation:
1. Trilok and Jayanth have sons (Gagan, Sumanth) and are the accountant and the lawyer; Venkat and Murali have daughters (Neetu, Teena) and are the sales executive and the doctor.
2. Gagan is not Jayanth's son, so Gagan is Trilok's son and Sumanth is Jayanth's. Sumanth's father is not the accountant, so Jayanth is the lawyer and Trilok the accountant.
3. Teena is not Murali's daughter, so Teena is Venkat's and Neetu is Murali's. Neetu is not the doctor's daughter, so Murali is the sales executive and Venkat the doctor.
4. So Teena's father is Venkat, the doctor.

Teacher's Note:
1. Split the people into groups first (fathers of sons vs fathers of daughters); it halves the possibilities at once.
2. Use each negative clue inside its small group, where a single 'not' immediately fixes the pairing.

Question 10: Directions: A, B, C, D and E are five cultural programmes to be performed, one on each day from Monday to Saturday (so one day is a holiday), on the following conditions. Monday is not a holiday and A is not performed on Tuesday. If A is performed on a day, the previous day must be a holiday. Between A and C there must be two programmes. E is followed immediately by D.

Which day is a holiday?
(a) Monday
(b) Wednesday
(c) Thursday
(d) Tuesday
Show Answer & Explanation

Answer: (d) Tuesday

Explanation:
1. A needs a holiday just before it, so A cannot be on Monday; it is not on Tuesday either.
2. Exactly two programmes (holiday not counted) must lie between A and C. Trying A on Thursday or Saturday leaves only one programme between A and C, so A is on Wednesday with Tuesday a holiday.
3. Then C is on Saturday, E and D take Thursday and Friday (E before D), and B is on Monday: B, holiday, A, E, D, C.

Teacher's Note:
1. Place the most restricted item first (here A, which drags a holiday with it), then fit the others around it.
2. Read counting conditions carefully: a holiday is not a programme, so it is not counted in 'between' conditions.

Question 11: Directions: A, B, C, D and E are five cultural programmes to be performed, one on each day from Monday to Saturday (so one day is a holiday), on the following conditions. Monday is not a holiday and A is not performed on Tuesday. If A is performed on a day, the previous day must be a holiday. Between A and C there must be two programmes. E is followed immediately by D.

On which day is A performed?
(a) Monday
(b) Wednesday
(c) Thursday
(d) Tuesday
Show Answer & Explanation

Answer: (b) Wednesday

Explanation:
1. A needs a holiday just before it, so A cannot be on Monday; it is not on Tuesday either.
2. Exactly two programmes (holiday not counted) must lie between A and C. Trying A on Thursday or Saturday leaves only one programme between A and C, so A is on Wednesday with Tuesday a holiday.
3. Then C is on Saturday, E and D take Thursday and Friday (E before D), and B is on Monday: B, holiday, A, E, D, C.

Teacher's Note:
1. Place the most restricted item first (here A, which drags a holiday with it), then fit the others around it.
2. Read counting conditions carefully: a holiday is not a programme, so it is not counted in 'between' conditions.

Question 12: Directions: A, B, C, D and E are five cultural programmes to be performed, one on each day from Monday to Saturday (so one day is a holiday), on the following conditions. Monday is not a holiday and A is not performed on Tuesday. If A is performed on a day, the previous day must be a holiday. Between A and C there must be two programmes. E is followed immediately by D.

What is the correct order of the programmes?
(a) E, D, A, B, C
(b) E, A, D, B, C
(c) A, E, D, B, C
(d) B, A, E, D, C
Show Answer & Explanation

Answer: (d) B, A, E, D, C

Explanation:
1. A needs a holiday just before it, so A cannot be on Monday; it is not on Tuesday either.
2. Exactly two programmes (holiday not counted) must lie between A and C. Trying A on Thursday or Saturday leaves only one programme between A and C, so A is on Wednesday with Tuesday a holiday.
3. Then C is on Saturday, E and D take Thursday and Friday (E before D), and B is on Monday: B, holiday, A, E, D, C.

Teacher's Note:
1. Place the most restricted item first (here A, which drags a holiday with it), then fit the others around it.
2. Read counting conditions carefully: a holiday is not a programme, so it is not counted in 'between' conditions.

Question 13: Directions: A college principal wishes to select four members of a faculty-student committee as representatives for the institute's Silver Jubilee Celebrations. The faculty members are Anup, Bhavya, Chetan and Divya and the students are Rohit, Sandeep, Tanuja and Usha. The selection must satisfy these conditions:
(1) The team of four members must have exactly two faculty members and two students.
(2) Either Anup or Bhavya must be one of the representatives, but both Anup and Bhavya cannot be representatives.
(3) If Rohit is a representative, Chetan must also be selected.
(4) If Tanuja is selected, Bhavya cannot be a representative.

If Rohit is selected, who among the following cannot be selected?
(a) Chetan
(b) Usha
(c) Sandeep
(d) Divya
Show Answer & Explanation

Answer: (d) Divya

Explanation:
1. Rohit forces Chetan into the team.
2. One of Anup or Bhavya must also be there, so both faculty places are filled by Chetan and Anup/Bhavya.
3. No faculty place is left, so Divya cannot be selected.

Teacher's Note:
1. Turn each 'if ... then' condition into a quick check and test every option against all of them.
2. In 'exactly one of two' conditions, one member of the pair always takes a fixed slot, which leaves very little room for others.

Question 14: Directions: A college principal wishes to select four members of a faculty-student committee as representatives for the institute's Silver Jubilee Celebrations. The faculty members are Anup, Bhavya, Chetan and Divya and the students are Rohit, Sandeep, Tanuja and Usha. The selection must satisfy these conditions:
(1) The team of four members must have exactly two faculty members and two students.
(2) Either Anup or Bhavya must be one of the representatives, but both Anup and Bhavya cannot be representatives.
(3) If Rohit is a representative, Chetan must also be selected.
(4) If Tanuja is selected, Bhavya cannot be a representative.

If Bhavya, Divya and Sandeep are representatives, who will be the other member in the team?
(a) Usha
(b) Rohit
(c) Chetan
(d) Divya
Show Answer & Explanation

Answer: (a) Usha

Explanation:
1. Two faculty (Bhavya, Divya) are already in, so the fourth member is a student.
2. Tanuja is ruled out because Bhavya is in; Rohit is ruled out because he needs Chetan, and no faculty place is left.
3. The fourth member is Usha.

Teacher's Note:
1. Turn each 'if ... then' condition into a quick check and test every option against all of them.
2. In 'exactly one of two' conditions, one member of the pair always takes a fixed slot, which leaves very little room for others.

Question 15: Directions: A college principal wishes to select four members of a faculty-student committee as representatives for the institute's Silver Jubilee Celebrations. The faculty members are Anup, Bhavya, Chetan and Divya and the students are Rohit, Sandeep, Tanuja and Usha. The selection must satisfy these conditions:
(1) The team of four members must have exactly two faculty members and two students.
(2) Either Anup or Bhavya must be one of the representatives, but both Anup and Bhavya cannot be representatives.
(3) If Rohit is a representative, Chetan must also be selected.
(4) If Tanuja is selected, Bhavya cannot be a representative.

If neither Sandeep nor Usha is represented, which of the following faculty must be in the team?
(a) Bhavya and Chetan
(b) Anup and Chetan
(c) Anup and Divya
(d) Anup and Bhavya
Show Answer & Explanation

Answer: (b) Anup and Chetan

Explanation:
1. The two students must then be Rohit and Tanuja.
2. Rohit requires Chetan; Tanuja rules out Bhavya, so Anup must be the Anup/Bhavya member.
3. The faculty pair is Anup and Chetan.

Teacher's Note:
1. Turn each 'if ... then' condition into a quick check and test every option against all of them.
2. In 'exactly one of two' conditions, one member of the pair always takes a fixed slot, which leaves very little room for others.

Question 16: Directions: K, L, M, N, O and P are six doctors. Each of them is required to present a paper on AIDS in a symposium. Three papers will be presented in the morning session before the lunch break and the other three in the afternoon session, subject to the following conditions:
(1) L's presentation must immediately precede M's presentation, and their presentations cannot be separated by the lunch break.
(2) N must be either the first or the last in the order of presenters.

If M has to be the fifth in the order of presenters, then what is the order of L?
(a) First
(b) Second
(c) Third
(d) Fourth
Show Answer & Explanation

Answer: (d) Fourth

Explanation:
1. L must come immediately before M.
2. M is 5th, so L is 4th; slots 4 and 5 are both in the afternoon, so the lunch break does not separate them.

Teacher's Note:
1. Draw six slots with a break between slots 3 and 4; a 'block' of two can never straddle that break.
2. Place fixed-end items (first or last) and blocks before the free items.

Question 17: Directions: K, L, M, N, O and P are six doctors. Each of them is required to present a paper on AIDS in a symposium. Three papers will be presented in the morning session before the lunch break and the other three in the afternoon session, subject to the following conditions:
(1) L's presentation must immediately precede M's presentation, and their presentations cannot be separated by the lunch break.
(2) N must be either the first or the last in the order of presenters.

If P and O are fifth and sixth respectively in the order, which of the following must be true?
(a) K is first
(b) K is third
(c) K is fourth
(d) M is fourth
Show Answer & Explanation

Answer: (c) K is fourth

Explanation:
1. N cannot be last (O is 6th), so N is first.
2. The L-M block cannot use slots 3-4 (lunch break) and slots 4-5 are blocked by P, so L-M take slots 2-3.
3. The only slot left, 4th, goes to K.

Teacher's Note:
1. Draw six slots with a break between slots 3 and 4; a 'block' of two can never straddle that break.
2. Place fixed-end items (first or last) and blocks before the free items.

Question 18: Directions: In a parking lot there are six parking slots in a row numbered 1 to 6 consecutively. Exactly five cars of five different colours, blue, green, maroon, red and white, are to be parked in the slots according to the following conditions:
(1) The red car must be parked in slot 3.
(2) The blue car must be parked in the slot next to the slot in which the white car is parked.
(3) The green car cannot be parked in a slot next to the slot in which the maroon car is parked.

If the white car is parked in slot 2, which of the following must be true?
(a) The blue car is parked in a slot next to the maroon car
(b) The maroon car is parked next to red
(c) The green car is parked next to blue
(d) None of the cars is parked in slot number 5
Show Answer & Explanation

Answer: (d) None of the cars is parked in slot number 5

Explanation:
1. Slot 3 is red, so blue (next to white in 2) must be in slot 1.
2. Green and maroon go into slots 4, 5, 6 without being adjacent, so they take 4 and 6.
3. Slot 5 is therefore empty.

Teacher's Note:
1. With five cars in six slots, track the empty slot as if it were a sixth item.
2. For 'must be true' questions, look for one arrangement that breaks an option; the option no arrangement can break is the answer.

Question 19: Directions: In a parking lot there are six parking slots in a row numbered 1 to 6 consecutively. Exactly five cars of five different colours, blue, green, maroon, red and white, are to be parked in the slots according to the following conditions:
(1) The red car must be parked in slot 3.
(2) The blue car must be parked in the slot next to the slot in which the white car is parked.
(3) The green car cannot be parked in a slot next to the slot in which the maroon car is parked.

In which of the following slots can the maroon car not be parked?
(a) 1
(b) 2
(c) 4
(d) 5
Show Answer & Explanation

Answer: (d) 5

Explanation:
1. If maroon is in 5, green cannot be in 4 or 6, so green is in 1 or 2.
2. The slots left (from 1, 2, 4, 6) then contain no two adjacent free slots for blue and white.
3. Maroon fits in 1, 2 or 4 (for example blue-white in 4-5, green in 6 with maroon in 1), but never in 5.

Teacher's Note:
1. With five cars in six slots, track the empty slot as if it were a sixth item.
2. For 'must be true' questions, look for one arrangement that breaks an option; the option no arrangement can break is the answer.

Question 20: Directions: In a parking lot there are six parking slots in a row numbered 1 to 6 consecutively. Exactly five cars of five different colours, blue, green, maroon, red and white, are to be parked in the slots according to the following conditions:
(1) The red car must be parked in slot 3.
(2) The blue car must be parked in the slot next to the slot in which the white car is parked.
(3) The green car cannot be parked in a slot next to the slot in which the maroon car is parked.

If the green car is parked in slot 2, which of the following slots remains vacant?
(a) 1
(b) 3
(c) 4
(d) 5
Show Answer & Explanation

Answer: (a) 1

Explanation:
1. Maroon cannot be in 1 (next to green in 2), so maroon is in 4, 5 or 6.
2. Blue and white need two adjacent slots: 4-5 (maroon 6) or 5-6 (maroon 4).
3. In every case slot 1 stays empty.

Teacher's Note:
1. With five cars in six slots, track the empty slot as if it were a sixth item.
2. For 'must be true' questions, look for one arrangement that breaks an option; the option no arrangement can break is the answer.

Question 21: Directions: In a parking lot there are six parking slots in a row numbered 1 to 6 consecutively. Exactly five cars of five different colours, blue, green, maroon, red and white, are to be parked in the slots according to the following conditions:
(1) The red car must be parked in slot 3.
(2) The blue car must be parked in the slot next to the slot in which the white car is parked.
(3) The green car cannot be parked in a slot next to the slot in which the maroon car is parked.

Which of the following must be true of any acceptable parking arrangement?
(a) There is an empty slot next to the green car.
(b) There is an empty slot next to the white car.
(c) Either the blue car or the white car is parked in a slot next to 3.
(d) One of the cars is parked in slot number 6.
Show Answer & Explanation

Answer: (d) One of the cars is parked in slot number 6.

Explanation:
1. If slot 6 were empty, the four cars would occupy 1, 2, 4, 5, which form two adjacent pairs (1-2 and 4-5).
2. Blue-white would take one pair and green-maroon would be forced into the other pair, making them adjacent, which is not allowed.
3. So slot 6 is always occupied; the other options fail, e.g. blue 1, white 2, green 4, empty 5, maroon 6.

Teacher's Note:
1. With five cars in six slots, track the empty slot as if it were a sixth item.
2. For 'must be true' questions, look for one arrangement that breaks an option; the option no arrangement can break is the answer.

Question 22: Directions: Three brothers Ranjit, Sailesh and Tushar are married to three sisters Archana, Bhargavi and Chandrika, but not in the same order.
(1) Chandrika has long hair.
(2) The dancer (one of the sisters) lives in Goa.
(3) The one married to Tushar is very fair.
(4) The sister with long hair does not like to write letters.
(5) Archana calls her dancer sister every Sunday.
(6) The sister in Pune is married to Tushar.
(7) Tushar's phone bills are high.
(8) Chandrika receives a letter from Goa once a week.
(9) The sister who does not like to write letters lives in Mysore.

Which sister lives in Pune?
(a) Archana
(b) Bhargavi
(c) Chandrika
(d) Data insufficient
Show Answer & Explanation

Answer: (a) Archana

Explanation:
1. Chandrika has long hair, so she does not write letters and therefore lives in Mysore.
2. Archana calls the dancer, so Archana is not the dancer; Chandrika lives in Mysore, not Goa. So Bhargavi is the dancer in Goa.
3. The remaining city, Pune, belongs to Archana, and the sister in Pune is married to Tushar.
4. So Archana lives in Pune.

Teacher's Note:
1. Chain the clues: a fact about one sister (long hair) often leads through two or three clues to her city.
2. Some clues are only colour (fairness, phone bills); identify and ignore them quickly.

Question 23: Directions: Three brothers Ranjit, Sailesh and Tushar are married to three sisters Archana, Bhargavi and Chandrika, but not in the same order.
(1) Chandrika has long hair.
(2) The dancer (one of the sisters) lives in Goa.
(3) The one married to Tushar is very fair.
(4) The sister with long hair does not like to write letters.
(5) Archana calls her dancer sister every Sunday.
(6) The sister in Pune is married to Tushar.
(7) Tushar's phone bills are high.
(8) Chandrika receives a letter from Goa once a week.
(9) The sister who does not like to write letters lives in Mysore.

Who is Chandrika's husband?
(a) Ranjit
(b) Sailesh
(c) Tushar
(d) Data incomplete
Show Answer & Explanation

Answer: (d) Data incomplete

Explanation:
1. Chandrika has long hair, so she does not write letters and therefore lives in Mysore.
2. Archana calls the dancer, so Archana is not the dancer; Chandrika lives in Mysore, not Goa. So Bhargavi is the dancer in Goa.
3. The remaining city, Pune, belongs to Archana, and the sister in Pune is married to Tushar.
4. Tushar is Archana's husband; Chandrika's husband is Ranjit or Sailesh, and no clue decides between them, so the data is incomplete.

Teacher's Note:
1. Chain the clues: a fact about one sister (long hair) often leads through two or three clues to her city.
2. Some clues are only colour (fairness, phone bills); identify and ignore them quickly.

Question 24: Directions: Three brothers Ranjit, Sailesh and Tushar are married to three sisters Archana, Bhargavi and Chandrika, but not in the same order.
(1) Chandrika has long hair.
(2) The dancer (one of the sisters) lives in Goa.
(3) The one married to Tushar is very fair.
(4) The sister with long hair does not like to write letters.
(5) Archana calls her dancer sister every Sunday.
(6) The sister in Pune is married to Tushar.
(7) Tushar's phone bills are high.
(8) Chandrika receives a letter from Goa once a week.
(9) The sister who does not like to write letters lives in Mysore.

Who is the dancer?
(a) Archana
(b) Bhargavi
(c) Chandrika
(d) Cannot be determined
Show Answer & Explanation

Answer: (b) Bhargavi

Explanation:
1. Chandrika has long hair, so she does not write letters and therefore lives in Mysore.
2. Archana calls the dancer, so Archana is not the dancer; Chandrika lives in Mysore, not Goa. So Bhargavi is the dancer in Goa.
3. The remaining city, Pune, belongs to Archana, and the sister in Pune is married to Tushar.
4. So the dancer is Bhargavi.

Teacher's Note:
1. Chain the clues: a fact about one sister (long hair) often leads through two or three clues to her city.
2. Some clues are only colour (fairness, phone bills); identify and ignore them quickly.

Question 25: Directions: Five women Madhurima, Kanchana, Chandana, Sahana and Roopa are married to a doctor, a naval officer, an advocate, a sales executive and an architect. Three of the women are an auditor, a lecturer and a doctor by profession, while the other two are housewives.
(1) Madhurima and Kanchana are not housewives and they are not married to either a doctor or an advocate.
(2) Roopa is not a doctor.
(3) Sahana and Roopa are neither a lecturer nor an auditor, and their husbands are neither an architect nor in the navy.
(4) Chandana is not a lecturer and the lecturer's husband is a naval officer.
(5) One husband and wife have the same profession.
(6) The sales executive is not Madhurima's or Chandana's husband. His wife is an auditor.

Who is the wife of the architect?
(a) Auditor
(b) Housewife
(c) Doctor
(d) Lecturer
Show Answer & Explanation

Answer: (b) Housewife

Explanation:
1. Roopa is not a lecturer, auditor or doctor, so she is a housewife. The auditor is married to the sales executive, who is not Madhurima's or Chandana's husband, and Sahana is not an auditor, so Kanchana is the auditor, married to the sales executive.
2. The lecturer is not Chandana, Sahana or Roopa, so Madhurima is the lecturer, married to the naval officer.
3. Chandana, Sahana and Roopa share the doctor, advocate and architect husbands; Sahana and Roopa cannot have the architect, so Chandana's husband is the architect.
4. The same-profession couple must be doctor-doctor, so Sahana is the doctor married to the doctor; Roopa (housewife) has the advocate and Chandana is a housewife.

Teacher's Note:
1. Keep two separate grids (wife's profession and husband's profession) and link them only through the 'married to' clues.
2. A clue like 'one couple has the same profession' only works for a profession that appears on both lists; here that is doctor.

Question 26: Directions: Five women Madhurima, Kanchana, Chandana, Sahana and Roopa are married to a doctor, a naval officer, an advocate, a sales executive and an architect. Three of the women are an auditor, a lecturer and a doctor by profession, while the other two are housewives.
(1) Madhurima and Kanchana are not housewives and they are not married to either a doctor or an advocate.
(2) Roopa is not a doctor.
(3) Sahana and Roopa are neither a lecturer nor an auditor, and their husbands are neither an architect nor in the navy.
(4) Chandana is not a lecturer and the lecturer's husband is a naval officer.
(5) One husband and wife have the same profession.
(6) The sales executive is not Madhurima's or Chandana's husband. His wife is an auditor.

Which of the following pairs is the correct husband-wife combination?
(a) Sales executive - Madhurima
(b) Architect - Chandana
(c) Advocate - Sahana
(d) Naval officer - Kanchana
Show Answer & Explanation

Answer: (b) Architect - Chandana

Explanation:
1. Roopa is not a lecturer, auditor or doctor, so she is a housewife. The auditor is married to the sales executive, who is not Madhurima's or Chandana's husband, and Sahana is not an auditor, so Kanchana is the auditor, married to the sales executive.
2. The lecturer is not Chandana, Sahana or Roopa, so Madhurima is the lecturer, married to the naval officer.
3. Chandana, Sahana and Roopa share the doctor, advocate and architect husbands; Sahana and Roopa cannot have the architect, so Chandana's husband is the architect.
4. The same-profession couple must be doctor-doctor, so Sahana is the doctor married to the doctor; Roopa (housewife) has the advocate and Chandana is a housewife.

Teacher's Note:
1. Keep two separate grids (wife's profession and husband's profession) and link them only through the 'married to' clues.
2. A clue like 'one couple has the same profession' only works for a profession that appears on both lists; here that is doctor.

Question 27: Directions: Five women Madhurima, Kanchana, Chandana, Sahana and Roopa are married to a doctor, a naval officer, an advocate, a sales executive and an architect. Three of the women are an auditor, a lecturer and a doctor by profession, while the other two are housewives.
(1) Madhurima and Kanchana are not housewives and they are not married to either a doctor or an advocate.
(2) Roopa is not a doctor.
(3) Sahana and Roopa are neither a lecturer nor an auditor, and their husbands are neither an architect nor in the navy.
(4) Chandana is not a lecturer and the lecturer's husband is a naval officer.
(5) One husband and wife have the same profession.
(6) The sales executive is not Madhurima's or Chandana's husband. His wife is an auditor.

Who is the wife of the naval officer?
(a) Roopa
(b) Chandana
(c) Madhurima
(d) Kanchana
Show Answer & Explanation

Answer: (c) Madhurima

Explanation:
1. Roopa is not a lecturer, auditor or doctor, so she is a housewife. The auditor is married to the sales executive, who is not Madhurima's or Chandana's husband, and Sahana is not an auditor, so Kanchana is the auditor, married to the sales executive.
2. The lecturer is not Chandana, Sahana or Roopa, so Madhurima is the lecturer, married to the naval officer.
3. Chandana, Sahana and Roopa share the doctor, advocate and architect husbands; Sahana and Roopa cannot have the architect, so Chandana's husband is the architect.
4. The same-profession couple must be doctor-doctor, so Sahana is the doctor married to the doctor; Roopa (housewife) has the advocate and Chandana is a housewife.

Teacher's Note:
1. Keep two separate grids (wife's profession and husband's profession) and link them only through the 'married to' clues.
2. A clue like 'one couple has the same profession' only works for a profession that appears on both lists; here that is doctor.

Question 28: Directions: Five women Madhurima, Kanchana, Chandana, Sahana and Roopa are married to a doctor, a naval officer, an advocate, a sales executive and an architect. Three of the women are an auditor, a lecturer and a doctor by profession, while the other two are housewives.
(1) Madhurima and Kanchana are not housewives and they are not married to either a doctor or an advocate.
(2) Roopa is not a doctor.
(3) Sahana and Roopa are neither a lecturer nor an auditor, and their husbands are neither an architect nor in the navy.
(4) Chandana is not a lecturer and the lecturer's husband is a naval officer.
(5) One husband and wife have the same profession.
(6) The sales executive is not Madhurima's or Chandana's husband. His wife is an auditor.

Who, among the following, is engaged in the doctor's profession along with her husband?
(a) Sahana
(b) Madhurima
(c) Chandana
(d) Roopa
Show Answer & Explanation

Answer: (a) Sahana

Explanation:
1. Roopa is not a lecturer, auditor or doctor, so she is a housewife. The auditor is married to the sales executive, who is not Madhurima's or Chandana's husband, and Sahana is not an auditor, so Kanchana is the auditor, married to the sales executive.
2. The lecturer is not Chandana, Sahana or Roopa, so Madhurima is the lecturer, married to the naval officer.
3. Chandana, Sahana and Roopa share the doctor, advocate and architect husbands; Sahana and Roopa cannot have the architect, so Chandana's husband is the architect.
4. The same-profession couple must be doctor-doctor, so Sahana is the doctor married to the doctor; Roopa (housewife) has the advocate and Chandana is a housewife.

Teacher's Note:
1. Keep two separate grids (wife's profession and husband's profession) and link them only through the 'married to' clues.
2. A clue like 'one couple has the same profession' only works for a profession that appears on both lists; here that is doctor.

Question 29: Directions: Six daughters of the Kapoor family, Anitha (A), Babitha (B), Haritha (H), Kavitha (K), Mamatha (M) and Sunitha (S), were all born on the same date and month, but each was born in a different year during a consecutive period of six years.
(1) H is younger than A.
(2) Both K and M are younger than B.
(3) K is two years younger than S.
(4) A was born either in 1992 or 1993.
(5) The oldest member of the group was born in 1990.

If A was born in 1992, then which of the following must also be true?
(a) B was born in 1990
(b) M was born in 1993
(c) S was born in 1991
(d) H was born in 1993
Show Answer & Explanation

Answer: (a) B was born in 1990

Explanation:
1. With A in 1992, the S-K pair (2 years apart) can be 1991-1993 or 1993-1995.
2. Only B or S can be the oldest (K, M, H are younger than someone). If S were 1990, K would be 1992, A's year, so S is not 1990.
3. So B was born in 1990 in every valid case; M and H vary.

Teacher's Note:
1. Write the six years 1990-1995 as slots; 'younger' means a later year.
2. Place the pair with a fixed gap (K two years after S) in every possible way and reject cases that break the other clues.

Question 30: Directions: Six daughters of the Kapoor family, Anitha (A), Babitha (B), Haritha (H), Kavitha (K), Mamatha (M) and Sunitha (S), were all born on the same date and month, but each was born in a different year during a consecutive period of six years.
(1) H is younger than A.
(2) Both K and M are younger than B.
(3) K is two years younger than S.
(4) A was born either in 1992 or 1993.
(5) The oldest member of the group was born in 1990.

If A is younger than K, which of the following statements need not be true?
(a) K was born in 1992
(b) M was born in 1994
(c) B was born in 1991
(d) A was born in 1993
Show Answer & Explanation

Answer: (b) M was born in 1994

Explanation:
1. A is younger than K and A is 1992 or 1993; K = S + 2, so K is at least 1992, giving K 1992 and A 1993.
2. Then S is 1990, B is 1991, and H and M take 1994 and 1995 in either order.
3. So M could be 1994 or 1995: 'M was born in 1994' need not be true.

Teacher's Note:
1. Write the six years 1990-1995 as slots; 'younger' means a later year.
2. Place the pair with a fixed gap (K two years after S) in every possible way and reject cases that break the other clues.

Question 31: Directions: Six daughters of the Kapoor family, Anitha (A), Babitha (B), Haritha (H), Kavitha (K), Mamatha (M) and Sunitha (S), were all born on the same date and month, but each was born in a different year during a consecutive period of six years.
(1) H is younger than A.
(2) Both K and M are younger than B.
(3) K is two years younger than S.
(4) A was born either in 1992 or 1993.
(5) The oldest member of the group was born in 1990.

If S was born in 1992, which of the following must be true?
(a) M was born in 1990
(b) K was born in 1995
(c) K was born in 1994
(d) B was born in 1991
Show Answer & Explanation

Answer: (c) K was born in 1994

Explanation:
1. K is two years younger than S, so K was born in 1994.
2. Then A is 1993, B (older than K and M) is 1990, M is 1991, H is 1995.

Teacher's Note:
1. Write the six years 1990-1995 as slots; 'younger' means a later year.
2. Place the pair with a fixed gap (K two years after S) in every possible way and reject cases that break the other clues.

Question 32: Directions: A Lions club's board of directors, composed of four women Kirthi, Latha, Maya and Neetu and three men Ram, Shyam and Tom, holds frequent meetings. A meeting can be held at Latha's, Neetu's or Shyam's house.
(1) Neetu cannot attend any meeting at Latha's house.
(2) Maya cannot attend any meeting on Tuesday or on Friday.
(3) Kirthi cannot attend any meeting at Neetu's house.
(4) Ram can attend only those meetings that Tom attends.
(5) Shyam can attend only those meetings that both Kirthi and Maya attend.

If all the members of the board have to attend a particular meeting, on which day and in whose house should it be held?
(a) Monday at Latha's house
(b) Tuesday at Shyam's house
(c) Wednesday at Neetu's house
(d) Thursday at Shyam's house
Show Answer & Explanation

Answer: (d) Thursday at Shyam's house

Explanation:
1. Neetu rules out Latha's house and Kirthi rules out Neetu's house, so the meeting must be at Shyam's house.
2. Maya rules out Tuesday and Friday, so Thursday at Shyam's house is the only fit.

Teacher's Note:
1. List each person's restriction as a rule about place, day or another person, then strike out members one by one.
2. 'Can attend only if X attends' means X's absence removes that person too; watch such chain reactions.

Question 33: Directions: A Lions club's board of directors, composed of four women Kirthi, Latha, Maya and Neetu and three men Ram, Shyam and Tom, holds frequent meetings. A meeting can be held at Latha's, Neetu's or Shyam's house.
(1) Neetu cannot attend any meeting at Latha's house.
(2) Maya cannot attend any meeting on Tuesday or on Friday.
(3) Kirthi cannot attend any meeting at Neetu's house.
(4) Ram can attend only those meetings that Tom attends.
(5) Shyam can attend only those meetings that both Kirthi and Maya attend.

If Shyam attends a meeting on Thursday which is not held at his house, which of the following must be true?
(a) The group can include at most two women
(b) The meeting is at Latha's house
(c) Ram is not at the meeting
(d) Tom is not at the meeting
Show Answer & Explanation

Answer: (b) The meeting is at Latha's house

Explanation:
1. Shyam attends only when Kirthi and Maya attend, so Kirthi is present.
2. Kirthi cannot attend at Neetu's house, and it is not at Shyam's house, so it is at Latha's house.

Teacher's Note:
1. List each person's restriction as a rule about place, day or another person, then strike out members one by one.
2. 'Can attend only if X attends' means X's absence removes that person too; watch such chain reactions.

Question 34: Directions: A Lions club's board of directors, composed of four women Kirthi, Latha, Maya and Neetu and three men Ram, Shyam and Tom, holds frequent meetings. A meeting can be held at Latha's, Neetu's or Shyam's house.
(1) Neetu cannot attend any meeting at Latha's house.
(2) Maya cannot attend any meeting on Tuesday or on Friday.
(3) Kirthi cannot attend any meeting at Neetu's house.
(4) Ram can attend only those meetings that Tom attends.
(5) Shyam can attend only those meetings that both Kirthi and Maya attend.

If Maya and Kirthi attend a meeting but Tom is unable to attend, which of the following could be true?
(a) The meeting is held on Tuesday
(b) The meeting is held on Friday
(c) The meeting is held at Neetu's house
(d) The meeting is held at Shyam's house
Show Answer & Explanation

Answer: (d) The meeting is held at Shyam's house

Explanation:
1. Maya's presence rules out Tuesday and Friday.
2. Kirthi's presence rules out Neetu's house.
3. A meeting at Shyam's house remains possible (Tom's absence only removes Ram).

Teacher's Note:
1. List each person's restriction as a rule about place, day or another person, then strike out members one by one.
2. 'Can attend only if X attends' means X's absence removes that person too; watch such chain reactions.

Question 35: Directions: A Lions club's board of directors, composed of four women Kirthi, Latha, Maya and Neetu and three men Ram, Shyam and Tom, holds frequent meetings. A meeting can be held at Latha's, Neetu's or Shyam's house.
(1) Neetu cannot attend any meeting at Latha's house.
(2) Maya cannot attend any meeting on Tuesday or on Friday.
(3) Kirthi cannot attend any meeting at Neetu's house.
(4) Ram can attend only those meetings that Tom attends.
(5) Shyam can attend only those meetings that both Kirthi and Maya attend.

If Tom is unable to attend a meeting on Tuesday at Neetu's house, what is the largest possible number of board members who can attend?
(a) 1
(b) 2
(c) 3
(d) 4
Show Answer & Explanation

Answer: (b) 2

Explanation:
1. Out: Tom (unable), Ram (needs Tom), Maya (Tuesday), Kirthi (Neetu's house), and Shyam (needs Kirthi and Maya).
2. Only Latha and Neetu can attend, so the maximum is 2.

Teacher's Note:
1. List each person's restriction as a rule about place, day or another person, then strike out members one by one.
2. 'Can attend only if X attends' means X's absence removes that person too; watch such chain reactions.

Question 36: Directions: Ten models are standing in a straight line numbered 1 to 10 for a fashion parade. Each one of them is wearing a sari of a different colour. One is in white, two are in different shades of blue, three are in different shades of pink, and the remaining four are wearing different shades of green.
(1) A model in a pink sari is not standing next to the model in the white sari.
(2) A model in a green sari is not standing next to a model in a blue sari.
(3) The two models wearing blue saris are adjacent to each other.
(4) Two models in pink saris are one at the beginning and one at the end.

If a model in a pink sari is in position 2 and the models in green are in positions 3 and 4, then in which position is the model in the white sari standing?
(a) Fifth
(b) Sixth
(c) Seventh
(d) Eighth
Show Answer & Explanation

Answer: (c) Seventh

Explanation:
1. Pinks are at 1, 2 and 10, so positions 5-9 hold white, two blues and two greens.
2. The blue pair cannot touch green; it must sit at 8-9 (next to pink at 10) with white at 7 as a buffer from the greens.
3. Order: P P G G G G W B B P, so white is 7th.

Teacher's Note:
1. Write positions 1-10, fix the given colours, and note which colours may never be neighbours.
2. The blue pair cannot touch green, so it must be bordered by white or pink; use that to locate it quickly.

Question 37: Directions: Ten models are standing in a straight line numbered 1 to 10 for a fashion parade. Each one of them is wearing a sari of a different colour. One is in white, two are in different shades of blue, three are in different shades of pink, and the remaining four are wearing different shades of green.
(1) A model in a pink sari is not standing next to the model in the white sari.
(2) A model in a green sari is not standing next to a model in a blue sari.
(3) The two models wearing blue saris are adjacent to each other.
(4) Two models in pink saris are one at the beginning and one at the end.

If a model in pink is in the third position and a model in blue is in the fourth position, then what is the position of the model in the white sari?
(a) Second
(b) Fifth
(c) Sixth
(d) Seventh
Show Answer & Explanation

Answer: (c) Sixth

Explanation:
1. Blue at 4 cannot have green at 5, and pink cannot be next to white; the second blue must be at 5 (position 3 is pink).
2. Position 6 cannot be green (next to blue) or pink, so it is white.
3. Order: P G P B B W G G G P, so white is 6th.

Teacher's Note:
1. Write positions 1-10, fix the given colours, and note which colours may never be neighbours.
2. The blue pair cannot touch green, so it must be bordered by white or pink; use that to locate it quickly.

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