CAT 2001 Question Paper
For the following questions answer them individually
Eight people carrying food baskets are going for a picnic on motorcycles.
Their names are A, B, C, D, E, F, G, and H. They have 4 motorcycles M1, M2, M3 and M4 among them. They also have 4 food baskets O, P, Q and R of different sizes and shapes and each can be carried only on motorcycles M1, M2, M3 and M4 respectively.
No more than 2 persons can travel on a motorcycle and no more than one basket can be carried on a motorcycle. There are 2 husband-wife pairs in this group of 8 people and each pair will ride on a motorcycle together.
C cannot travel with A or B. E cannot travel with B or F. G cannot travel with F, or H, or D.
The husband-wife pairs must carry baskets O and P. Q is with A and P is with D.
F travels on M1 and E travels on M2 motorcycles.
G is with Q, and B cannot go with R.
Who is travelling with H?
In a family gathering there are 2 males who are grandfathers and 4 males who are fathers. In the same gathering there are 2 females who are grandmothers and 4 females who are mothers. There is at least one grandson or a granddaughter present in this gathering. There are 2 husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (whose wife is not present) has 2 grandsons and a son present. The single grandmother (whose husband is not present) has 2 grand daughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or granddaughter present. What is the minimum number of people present in this gathering?
I have a total of Rs. 1,000. Item A costs Rs. 110, item B costs Rs. 90, item C costs Rs. 70, item D costs Rs. 40 and item E costs Rs. 45. For every item D that I purchase, I must also buy two of item B. For every item A, I must buy one of item C. For every item E, I must also buy two of item D and one of item B. For every item purchased I earn 1,000 points and for every rupee not spent I earn a penalty of 1,500 points. My objective is to maximise the points I earn. What is the number of items that I must purchase to maximise my points?
Four friends Ashok, Bashir, Chirag and Deepak are out for shopping. Ashok has less money than three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an amount equal to the difference of amounts with Bashir and Chirag. Ashok has three times the money with Deepak. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket that are priced Rs. 200, Rs. 400, Rs. 600, and Rs. 1,000 a piece respectively. Chirag borrows Rs. 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs. 100 from Ashok and is left with no money. Ashok buys three shirts. What is the costliest item that Deepak could buy with his own money?
In a ‘keep-fit’ gymnasium class there are 15 females enrolled in a weight-loss programme. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4, or W5. One instructor is assigned to one weight-group only.
Sonali, Shalini, Shubhra and Shahira belong to the same weight-group.
Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group.
Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight groups.
Somya cannot be with Ritu, and Tara cannot be with Radha.
Komal cannot be with Radha, Somya, or Ritu.
Shahira is in W1 and Somya is in W4 with Ruchika.
Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four.
No weight-group can have more than five or less than one member.
Amita, Babita, Chandrika, Deepika and Elina are instructors of weight-groups with membership sizes 5, 4, 3, 2 and 1 respectively. Who is the instructor of Radha?
A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected.
M1 likes fishing and smoking, but hates gambling.
M2 likes smoking and drinking, but hates fishing.
M3 likes gambling, but hates smoking,
M4 likes mountaineering, but hates drinking,
M5 likes drinking, but hates smoking and mountaineering.
M6 likes fishing, but hates smoking and mountaineering.
M7 likes gambling and mountaineering, but hates fishing.
M8 likes smoking and gambling, but hates mountaineering.
Who are the four people selected by the king?
Directions for the following four questions: Answer the questions based on the following information.
A and B are two sets (e.g. A = Mothers, B = Women).
The elements that could belong to both the sets (e.g. women who are mothers) is given by the set $$C = A \cap B$$.
The elements which could belong to either A or B, or both, is indicated by the set $$D = A \cup B$$ .
A set that does not contain any elements is known as a null set represented by $$\phi$$(e.g. if none of the women in the set B is a mother, then $$C = A \cap B$$ is a null set, or C = $$\phi$$).
Let ‘V’ signify the set of all vertebrates, ‘M’ the set of all mammals, ‘D’ dogs, ‘F’ fish, ‘A’ alsatian and ‘P’, a dog named Pluto.
