Prof. Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities – lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule MUST satisfy the following restrictions:
She conducts quizzes on exactly three mornings.
If she conducts quizzes on Monday, she does not conduct a quiz on Tuesday.
She lectures in the afternoon on exactly two consecutive calendar days.
She evaluates quizzes on exactly one morning and three afternoons.
She works on consultancy project on exactly one morning.
On Saturday, she neither lectures nor conducts quizzes.

Which one of the following must be a day on which Professor lectures?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
E. Saturday

On Wednesdays, the Professors could be scheduled to
A. Work on a consultancy project in the morning and conduct a quiz in the afternoon
B. Lecturer in the morning and evaluate quizzes in the afternoon
C. Conduct a quiz in the morning and lecture in the afternoon
D. Conduct a quiz in the morning and work on consultancy project in the afternoon
E. Evaluate quizzes in the morning and evaluate quizzes in the afternoons

Which one of the following statements must be true?
A. There is one day on which she evaluates quizzes both in the morning and in the afternoon.
B. She works on consultancy project on one of the days on which she lectures.
C. She works on consultancy project on one of the days on which she evaluates quizzes.
D. She lectures on one of the days on which she conducts quiz.
E. She lecturers on one of the days on which she evaluates quizzes.

If the Professor conducts a quiz on Tuesday, then her schedule for evaluating quizzes could be
A. Monday morning, Monday afternoon, Friday morning, Friday afternoon.
B. Monday morning, Friday afternoon, Saturday morning, Saturday afternoon
C. Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon
D. Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon
E. Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon

There are exactly ten stores and no other buildings on a straight street. On the northern side of the street, from West to East, are stores 1, 3, 5, 7 and 9; on the southern side of the street, also from West to east, are stores 2, 4, 6, 8 and 10. The stores on the northern side are located directly across the street from those on the southern side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colours: green, red, and yellow. The stores have been decorated with lights according to the following conditions:
No store is decorated with lights of the same colour as those of any store adjacent to it.
No store is decorated with lights of the same colour as those of the store directly cross the street from it.
Yellow lights decorate exactly one store on each side of the street.
Red lights decorate store 4.
Yellow lights decorate store 5.

Which one of the following could be an accurate list of the colours of the lights that decorate stores 2, 4, 6, 8 and 10, respectively?
A. green, red, green, red, green
B. green, red, yellow, red, green
C. green, red, green, yellow, red
D. yellow, green, red, green, red
E. yellow, red, green, red, yellow

If green lights decorate store 7, then each of the following statements could be false EXCEPT:
A. Green lights decorate store 2
B. Green lights decorate store 10
C. Red lights decorate store 9
D. Red lights decorate store 8
E. Yellow lights decorate store 2

Suppose that yellow lights decorate exactly two stores on the south side of the street and exactly one store on the north side. If all other conditions remain the same, then which one of the following statements MUST be true?
A. Green lights decorate store 1
B. Red lights decorate store 7
C. Red lights decorate store 10
D. Yellow lights decorate store 2
E. Yellow lights decorate store 8

Which one of the following statements MUST be true?
A. Green lights decorate store 10
B. Red lights decorate store 1
C. Red lights decorate store 8
D. Yellow lights decorate store 8
E. Yellow lights decorate store 10

Six square states having equal area in a country are located in North – South direction in two columns next to each other. States are located in the given order, State 1, State 3, and State 5 are on the western side and State 2, State 4, and State 6 are on the eastern side. Within the six states, there are on the eastern side. Within the six states, there are exactly four medical institutes, two management institutes, and two technical institutes. These eight institutions are located as follows:
No institution is in more than one of the states.
None of the states contains more than one management institute, and none contains more than one technical institute.
None of the states contains both a management institute and a technical institute.
Each management institute is located in a state that contains at least one medical institute.
The technical institutes are located in two states that do not share a common boundary.
State 3 contains a technical institute, and
State 6 contains a management institute.

If one of the states contains exactly two medical institutes and exactly one technical institute, then which combination of three states might contain no medical institute?
A. 1, 3, 5
B. 1, 4, 5
C. 2, 3, 5
D. 2, 4, 6
E. 4, 5, 6

Which one of the following could be true?
A. Sate 1 contains exactly one medical institute
B. Sate 1 contains exactly one technical institute
C. Sate 2 contains exactly one management institute
D. State 5 contains exactly one technical institute
E. State 6 contains exactly one technical institute

A complete and accurate list of the states, any one of which could contain the management institute that is not in State 6, would be _______
A. 1, 4
B. 1, 4, 5
C. 2, 4
D. 1, 2, 4, 5
E. 4, 5

If each of the six states contains at least one of the eight institutions, then which one of the following must be true?
A. There is management institute in state 4
B. There is a management institute in state 1
C. There is a medical institute in state 2
D. There is a medical institute in state 3
E. There is a medical institute is state 4

A, B, C, D, E and F are a group of friends from a club. There are two housewives, one lecturer, one architect, one accountant and one lawyer in the group. There are two married couples in the group. The lawyer is married to D who is a housewife. No lady in the group is either an architect or an accountant. C, the accountant, is married to F who is a lecturer. A is married to D and E is not a housewife.

What is the profession of E?
a. Lawyer
b. Architect
c. Lecturer
d. Accountant

How many members of the group are male?
a. 2
b. 3
c. 4
d. None of these

Each digit, 1, 2, 3, 4, 5, 6, 7, 8 and 9 is represented by a different letter A, B, C, D, E, F, G, H and I but not necessarily in this order. Further, each of A + B + C, C + D + E, E + F + G and G + H + I is equal to 13.
Determine the value of each of the alphabets such that the above conditions are satisfied.

A survey is conducted in a school among 150 students and it was found that 100 students play cricket, 90 students play football and 80 students play hockey. As physical education was given emphasis in the school, every student had to play at least one sport.
What can be the maximum number of students who play exactly two sports?
What can be the maximum number of students who play exactly one sport?

Prove or Disprove:

There exists some power of 3 which ends in 001.

How many 5 digit numbers are there such that the sum of its digits is odd?
Example: 12345 is a five digit number such that the sum of its digits = 1 + 2 + 3 + 4 + 5 = 15 = an odd number.

Prove that:
"In any group of 6 people, there are either 3 mutual friends or 3 mutual strangers".

Mr. A, Mr. B, Mr. C and Mr. D are four men who are Physicist, Mathematician, Doctor and Policeman, though not necessarily in that order. Mr. A and Mr. B are neighbours and they go together to their work by a bike. Mr. B makes more money than Mr. C. Mr. A meets Mr. D regularly in chess playing. The Physicist always goes by car. The only time the Doctor met the Policeman ever was when the Policeman arrested the Doctor for speeding. The policeman makes more money than the Mathematician. The Doctor makes more money than Mr. D

Who is the Physicist?
(a) Mr. A
(b) Mr. C
(c) Mr. D
(d) Mr. B
(e) Cannot be determined

Who is the second highest earner?
(a) Mr. C
(b) Mr. D
(c) Mr. A
(d) Either (a) or (b)
(e) Cannot be determined

Who is the Mathematician?
(a) Mr. A
(b) Mr. D
(c) Mr. B
(d) Mr. C
(e) Cannot be determined

What is the profession of Mr. B?
(a) Physicist
(b) Policeman
(c) Mathematician
(d) Doctor
(e) Cannot be determined

Let us suppose that there are 100 students in my class. Prove that among them there are at least two of them who have an equal number of friends.
Note: If A is friends with B then it also implies that B is friends with A or else A and B both are strangers to each other.

In a street there are 5 houses painted 5 different colours. In each house lives a person of a different nationality. The 5 homeowners each drink a different beverage, smoke a different brand of cigar, and keep a different pet.
1. The Brit lives in the Red house.
2. The Swede has a Dog.
3. The Dane drinks Tea.
4. The Green house is on the left of the White house.
5. The owner of the Green house drinks Coffee.
6. The person who smokes Pall Mall has Birds.
7. The owner of the Yellow house smokes Dunhill.
8. The man living in the center house drinks Milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who has Cats.
11. The man who has Horses lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks Beer.
13. The German smokes Prince.
14. The Norwegian lives next to the Blue house.
15. The man who smokes Blends has a neighbour who drinks water.

Find out the correct combination of drinks, pets, smokes and colour of the house for each of the five persons.

A very long hallway has 1000 doors numbered 1 to 1000; all doors are initially closed. One by one, 1000 people get into the hall; the first person opens each door, the second closes all door with even numbers, the third person closes door 3, opens door 6, closes door 9, opens door 12 etc. That is, the nth person changes all doors whose numbers are divisible by n. After all 1000 people have got into the hall, find out how many doors will remain open.

In the shooting of the movie, "A Beautiful Mind", Ravi, the actor, is running towards a vertical mirror with a speed of 10 m/sec on a line which is perpendicular to the plane of the mirror. The mirror is moving towards Ravi with a speed of 6 m/sec along the same line. Find the speed of Ravi’s image with respect to Ravi (the image of Ravi forms on the other side of the mirror such that the distance between the image of Ravi and the mirror is equal to the distance between Ravi and the mirror).

There are 60 workers who work for a company, out of which 25 are women. Also:
28 workers are married
26 workers are graduate
20 married workers are graduate of which 9 are men
15 men are graduate
15 men are married
How many unmarried women are graduates and how many unmarried women work in the company?

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

At what time do Ram and Shyam first meet each other?
(a) 10 a.m.
(b) 10:10 a.m.
(c) 10:20 a.m.
(d) 10:30 a.m.

At what time does Shyam overtake Ram?
(a) 10:20 a.m.
(b) 10:30 a.m.
(c) 10:40 a.m.
(d) 10:50 a.m.

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of the white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :
(a) 10
(b) 12
(c) 14
(d) 16

Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number 9 appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?
a. 10,000
b. 2,430
c. 3,402
d. 3,006

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.
• A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR
project alone. is equal to the volunteers having additional involvement in the ER project.
• The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
• 17 volunteers are involved in the TR project. ,
• The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project
alone.
• Ten volunteers involved in the TR project are also involved in at least one more project.

Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:
(a) 1
(b) 3
(c) 4
(d) 5

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
(a) Twenty volunteers are involved in FR.
(b) Four volunteers are involved in all the three projects.
(c) Twenty three volunteers are involved in exactly one project.
(d) No need for any additional information.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?
(a) The lowest number of volunteers is now in TR project.
(b) More volunteers are now in FR project as compared to ER project.
(c) More volunteers are now in TR project as compared to ER project.
(d) None of the above.

After the withdrawal of volunteers, as indicated in the above question, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?
(a) ER
(b) FR
(c) TR
(d) Cannot be determined

Five boys — A, B, C, D and E — went on a shopping trip. Before shopping, one boy had Rs. 400, one had Rs. 300, two boys had Rs. 200 each and one had Rs. 100. While shopping they did not lend or borrow from each other. After the shopping was over, it was observed that they were left with Rs. 165, Rs. 95, Rs. 70, Rs. 40 and Rs. 10, not necessarily in this order. Further, the following is known about the money they started with, they spent, or they were left with.
I. A started with more money than D.
II. B spent Rs. 15 more than C.
III. E started with more money than just one another person of the group.
IV. A spent the most but did not end with the least.
V. C started with 66.66% of the money that B started with.
VI. D spent the least and ended with more than A and C.
VII. E spent Rs. 35.

Who ended with the maximum amount of money?
a. A
b. B
c. C
d. E

How much money did A spend?
a. Rs. 205
b. Rs. 190
c. Rs. 35
d. Rs. 360

In ascending order of spending, E would rank at which position?
a. 1
b. 2
c. 4
d. 5

Who ended with Rs. 40?
a. A
b. B
c. C
d. D