CAT1990 Related Question Answers
27. Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is
29. If the dealer would have managed to get an additional space to stock 20 more items, then for maximizing profit, the ratio of number of VCRs and number of TVs that he should stock is
30. The maximum profit, in rupees lakh, the dealer can earn from his original stock if he can sell a colour TV at Rs. 12200 and VCR at Rs.18300 is
31.
Ghosh Babu has a certain amount of property consisting of cash, gold coins and silver bars. The cost of a gold coin is Rs. 4000 and the cost of a silver bar is Rs. 1000. Ghosh Babu distributed his property among his daughters equally. He gave to his eldest daughter gold coins worth 20% of the total property and Rs. 25000 in cash. The second daughter was given silver bars worth 20% of the remaining property and Rs. 50000 cash. He then gave each of the third and fourth daughters equal number of gold coins and silver bars both together accounting each for 20% of the property remaining after the previous distribution and Rs. 25000 more than what the second daughter had received in cash.The amount of property in gold and silver possessed by Ghosh Babu is
34.
The following questions relate to a game to be played by you and your friend. The game consists of a 4 x 4 board (see below) where each cell contains a positive integer. You and your friend make moves alternately. A move by any of the players consists of splitting the current board configuration into two equal halves and retaining one of them. In your moves you are allowed to split the board only vertically and to decide to retain either the left or the right half. Your friend, in his/her moves, can split the board only horizontally and can retain either the lower or the upper half. After two moves by each player a single cell will remain which can no longer be split and the number in that cell will be treated as the gain (in rupees) of the person who has started the game. A sample game is shown below. So your gain is Re.1. With the same initial board configuration as above and assuming that you have to make the first move, answer the following questions.
Initial Board 
After your move (retain left)
After your friends move (retain upper)
After your move (retain right)
After your friends move (retain lower)
If you choose (retain right) (retain left) in your turns, the best move sequence for your friend to reduce your gain to a minimum will be
36. If your first move is (retain right), then whatever moves your friend may select you can always force a gain of no less than
37. The roots of the equation $$ax^{2} + 3x + 6 = 0$$ will be reciprocal to each other if the value of a is
38. A car after traveling 18 km from a point A developed some problem in the engine and speed became 4/5 of its original speed As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B (in km.) is
39. A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs.94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.)
40. Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?
41. N the set of natural numbers is partitioned into subsets $$S_{1}$$ = $$(1)$$, $$S_{2}$$ = $$(2,3)$$, $$S_{3}$$ =$$(4,5,6)$$, $$S_{4}$$ = $${7,8,9,10}$$ and so on. The sum of the elements of the subset $$S_{50}$$ is
42. A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares such formed (in sq.cm.)is
43.
The pages of a book are numbered 0, 1, 2 . upto M, M>0. There are four categories of instructions that direct a person in positioning the book at a page. The instruction types and their meanings are :
1. OPEN : Position the book at page No. 1
2. CLOSE : Position the book at page No. 0
3. FORWARD, n :From the current page move forward by n pages; if, in this process, page number M is reached, stop at M.
4. BACKWARD, n : From the current page, move backward by n pages; if in this process, page number 0 is reached, stop at page number 0.
In each of the following questions, you will find a sequence of instructions formed from the above categories. In each case, let n1 be the page number before the instructions are executed and n2 be the page number at which the book is positioned after the instructions are executed.FORWARD, 25 ; BACKWARD, 10. which of the following statements is true?
44. BACKWARD, 5; FORWARD, 5. Which of the following statements is true about the above set of instructions?
45. FORWARD, 10; FORWARD, 10. Which of the following statements about the above instructions is true?
46. FORWARD, 5; BACKWARD, 4. Which of the following statements about the above instructions is true?
47.
There are 5 cities, A, B, C, D and E connected by 7 roads as shown in the figure below:
Design a route such that you start from any city of your choice and walk on each of the 7 roads once and only once, not necessarily returning to the city from which you started.For a route that satisfies the above restrictions, which of the following statements is true?
50. If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29th February. If we are to consider people born in 20th century (1901-2000) and assuming no deaths.
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