CAT 2001 Question Paper

What is the value of X?

I. X and Y are unequal positive even integers, less than 10, and $$\frac{X}{Y}$$ is an odd integer.

II. X and Y are positive even integers, each less than 10, and product of X and Y is 12.

On a given day a boat ferried 1,500 passengers across the river in 12 hr. How many round trips did it make?

I. The boat can carry 200 passengers at any time.

II. It takes 40 min each way and 20 min of waiting time at each terminal.

What will be the time for downloading software?

I. Transfer rate is 6 kilobytes per second.

II. The size of the software is 4.5 megabytes.

A square is inscribed in a circle. What is the difference between the area of the circle and that of the square?

I. The diameter of the circle is $$25 \sqrt{2}$$ cm.

II. The side of the square is $$25$$ cm.

Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy?

I. Ram bought one-half the number of apples that Gopal bought.

II. The wholesale dealer had a stock of 500 apples.

At a village mela, the following six nautankis (plays) are scheduled as shown in the table below.

You wish to see all the six nautankis. Further, you wish to ensure that you get a lunch break from

12.30 p.m. to 1.30 p.m. Which of the following ways can you do this?

Mrs Ranga has three children and has difficulty remembering their ages and months of their birth. The clue below may help her remember.
. The boy, who was born in June, is 7 years old.
. One of the children is 4 years old but it was not Anshuman.
. Vaibhav is older than Suprita.
. One of the children was born in September, but it was not Vaibhav.
. Suprita’s birthday is in April.
. The youngest child is only 2-year-old.
Based on the above clues, which one of the following statements is true?

The Bannerjees, the Sharmas, and the Pattabhiramans each have a tradition of eating Sunday lunch as a family. Each family serves a special meal at a certain time of day. Each family has a particular set of chinaware used for this meal. Use the clues below to answer the following question.
. The Sharma family eats at noon.
. The family that serves fried brinjal uses blue chinaware.
. The Bannerjee family eats at 2 o’clock.
. The family that serves sambar does not use red chinaware.
. The family that eats at 1 o’clock serves fried brinjal.
. The Pattabhiraman family does not use white chinaware.
. The family that eats last likes makkai-ki-roti.
Which one of the following statements is true?

While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the counter and ran out. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really did not want to help Balbir. So each of them made a statement which contained one truth and one lie.

. Shopkeeper number 1 said: “The dog had black hair and a long tail.”

. Shopkeeper number 2 said: “The dog had a short tail and wore a collar.”

. Shopkeeper number 3 said: “The dog had white hair and no collar.”

Based on the above statements, which of the following could be a correct description?

On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:

The number of red oak leaves with spots is even and positive.

The number of red oak leaves without any spot equals the number of red maple leaves without spots.

All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.

There are no spotted maple leaves that are not red.

There are exactly 6 red spotted maple leaves.

There are exactly 22 maple leaves that are neither spotted nor red.

How many oak leaves did she collect?