CAT Previous Paper 2006 Online Test

1. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

2. The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and the height are halved while the length is doubled, then the total area of the four walls of the room will

3. A airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of the luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.
What is the free luggage allowance?

4. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

5. Consider a sequence where the n^th term, t_n = n/(n + 2), n = 1, 2 ........ The value of t₃ x t₄ x t₅ x .... t₅₃ equals:

6. When you reserve the digits of the number 13, the number increases by 18. How many other two-digit number increase by 18 when their digits are reserved?

7. What values of x satisfy x^2/3 + x^1/3 - 2 ≤ 0?

8. What are the values of x and y that satisfy both the equations?
2^0.7x . 3^-1.25y = 8√6/27
4^0.3x . 9^0.2y = 8 . (81)^1/5

9. There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

10. Which among 2^1/2, 3^1/3, 4^1/4, 6^1/6, and 12^1/12, is the largest?

11. If log_y X = (a. log_zy) = (b. log_xz) = ab, then which of the following pairs of values for (a, b)is not possible?

12. A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square:

Find the area of the part of the circle (round punch) falling outside the square sheet.

13. A airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of the luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.
What is the weight of Praja's luggage?

14. Consider the set = {1, 2, 3, ........, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

15. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

16. A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square:

The proportion of the sheet area the remains after punching is:

17. A semi circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi circle (in sq. cm) will be:

18. If x = -0.5, then which of the following has the smallest value?
2^1/x
1/x
1/x²
2^x
1/√-x

19. If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the what is the value of abc/def?

20. The number of solutions of the equation 2x + y  = 40 where both x and y are positive integers and x ≤ y is: