List of top Questions asked in CAT- 2001

In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. If he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

In some code, letters $a, b, c, d, e$ represent 2, 4, 5, 6, and 10 in some order. Given:
I. $a + c = e$,
II. $b - d = d$,
III. $e + a = b$.
Which is true?

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is:

Fresh grapes contain 90% water by weight while dried grapes contain 20% water. What is the weight of dry grapes available from 20 kg of fresh grapes?

Three classes X, Y and Z take an algebra test. - Average score in X: 83.
- Average score in Y: 76.
- Average score in Z: 85.
- Average of X and Y together: 79.
- Average of Y and Z together: 81.
What is the average for all three classes?

Match the dictionary definitions (A–D) of the word “Relief” with the correct usage (E–H).

Dictionary definition		Usage
A. Removal or lightening of something distressing	E	A ceremony follows the relief of a sentry after the morning shift.
B. Aid in the form of necessities for the indigent	F	It was a relief to take off the tight shoes.
C. Diversion	G	The only relief I get is by playing cards.
D. Release from the performance of duty	H	Disaster relief was offered to the victims.

Arrange the sentences to form a coherent paragraph:
A. But in the industrial era destroying the enemy’s productive capacity means bombing the factories which are located in the cities.
B. So in the agrarian era, if you need to destroy the enemy’s productive capacity, what you want to do is burn his fields, or if you’re really vicious, salt them.
C. Now in the information era, destroying the enemy’s productive capacity means destroying the information infrastructure.
D. How do you do battle with your enemy?
E. The idea is to destroy the enemy’s productive capacity, and depending upon the economic foundation, that productive capacity is different in each case.
F. With regard to defence, the purpose of the military is to defend the nation and be prepared to do battle with its enemy.

Match the dictionary definitions (A–D) of the word “Infer” with the correct usage (E–H).

Dictionary definition		Usage
A. To derive by reasoning or implication	E	We see smoke and infer fire.
B. To surmise	F	Given some utterance, a listener may infer from it all sorts of things which neither the utterance nor the utterer implied.
C. To point out	G	I waited all day to meet him. From this you can infer my zeal to see him.
D. To hint	H	She did not take part in the debate except to ask a question inferring that she was not interested in the debate.

Arrange the sentences to form a coherent paragraph:
A. Passivity is not, of course, universal.
B. In areas where there are no lords or laws, or in frontier zones where all men go armed, the attitude of the peasantry may well be different.
C. So indeed it may be on the fringe of the unsubmissive.
D. However, for most of the soil-bound peasants the problem is not whether to be normally passive or active, but when to pass from one state to another.
E. This depends on an assessment of the political situation.

Match the dictionary definitions (A–D) of the word “Mellow” with the correct usage (E–H).

Dictionary definition		Usage
A. Adequately and properly aged so as to be free of harshness	E	He has mellowed with age.
B. Freed from the rashness of youth	F	The tones of the old violin were mellow.
C. Of soft and loamy consistency	G	Some wines are mellow.
D. Rich and full but free from stridency	H	Mellow soil found in the Gangetic plains.

A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. The total area of the walkway is 516 m$^2$. How wide, in metres, is the walkway?

If $a, b, c, d$ are four positive real numbers such that $abcd = 1$, what is the minimum value of $(1+a)(1+b)(1+c)(1+d)$?

A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is:

Three friends — Asit, Arnold and Afzal — work together to get chores done. Time together is 6 hr less than Asit alone, 1 hr less than Arnold alone, and half the time Afzal alone would take. How long did it take them together?

A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

For a Fibonacci sequence, from the third term onwards, each term is the sum of the previous two. If the difference in squares of the 7th and 6th terms is 517, what is the 10th term?

Train X departs from station A at 11 a.m. for station B, 180 km away. Train Y departs from station B at 11 a.m. for station A. Train X speed = 70 km/h, no stops. Train Y speed = 50 km/h, stops for 15 min at station C, 60 km from B. Ignoring train lengths, find the distance from A to meeting point.

Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom's steps. Shyama gets to the top after taking 25 steps, while Vyom takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?