Quantitative Aptitude Test CAT 2006
1. If x = −0.5, then which of the following has the smallest
value?
A.
B.
C.
D.
E.
2. Which among , is the
largest ?
A.
B.
C.
D.
E.
3. If
then
what is the value of
A.
B.
C.
D.
E.
4. The length, breadth and height of a room are in the ratio 3 :
2 : 1. If the breadth and height are halved while the length is doubled, then
the total area of the four walls of the room will
A. Remains the same
B. Decrease by 13.64%
C. Decrease by 15%
D. Decrease by 18.75%
E. Decrease by 30%
5. Consider a sequence where the nth term,
. The value of
equals:
A.
B.
C.
D.
E.
6. A group of 630 children is arranged in rows for a group
photograph session. Each row contains three fewer children than the row in front
of it. What number of rows is not possible?
A. 3
B. 4
C. 5
D. 6
E. 7
7. What are the values of x and y that satisfy both the
equations?
A. x = 2, y = 5
B. x = 2.5, y = 6
C. x = 3, y = 4
D. x = 3, y = 5
E. x = 5, y = 2
8. The number of solutions of the equation
2x + y = 40 where both x and y are positive integers and
is:
A. 7
B. 13
C. 14
D. 18
E. 20
9. A survey was conducted of 100 people to find out whether they
had read recent issues of Golmal, a monthly magazine. The summarized information
regarding readership in 3 months is given below:
What is the number of surveyed people who have read exactly two
consecutive issues (out of the three)?
A. 7
B. 9
C. 12
D. 14
E. 17
10. 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?
A. 21
B. 25
C. 41
D. 67
E. 73
11. The graph of y – x against y + x is as shown below.Then,
which of the options given shows the graph of y against x.
A.
B.
C.
D.
E.
12. Consider the set S = {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?
A. 3
B. 4
C. 6
D. 7
E. 8
Directions for questions 13 to 14
A punching machine is used to punch a circular hole of diameter
two units from a square sheet of aluminum 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
13. The proportion of the sheet area that remains after punching
is:
A.
B.
C.
D.
E.
14. Find the area of the part of the circle (round punch) falling
outside the square sheet.
A.
B.
C.
D.
E.
15. What values of x satisfy
A.
B.
C. 1<x<8
D.
E.
16. Let , where
x is any real number. Then the minimum possible value of (x) is:
A. 1/3
B. 1/2
C. 2/3
D. 4/3
E. 5/3
Directions for questions 17 and 18
17. What is the weight of Praja‘s luggage?
A. 20 kg
B. 25 kg
C. 30 kg
D. 35 kg
E. 40 kg
18. What is the free luggage allowance?
A. 10 kg
B. 15 kg
C. 20 kg
D. 25 kg
E. 30 kg
19. Arun, Barun and Kiranmala start from the same place and
travel in the same direction at speeds of 30 km/hr, 40 km/hr and 60 km/hr
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?
A. 3 hrs
B. 3.5 hrs
C. 4 hrs
D. 4.5 hrs
E. 5 hrs
20. When you reverse the digits of the number 13, the number
increases by 18. How many other two digit numbers increase by 18 when their
digits are reversed?
A. 5
B. 6
C. 7
D. 8
E. 10
21. A semicircle 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 semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the
semicircle (in sq. cm.) will be:
A.
B.
C.
D.
E. Cannot be determined
22. 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?
A. 144
B. 180
C. 192
D. 360
E. 716
23. 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:
A. 101 : 88
B. 87 : 100
C. 110 : 111
D. 85 : 98
E. 97 : 84
24. If
A.
B. 1, 1
C.
D. 0.4, 2.5
E. 2, 2
25. An equilateral triangle BPC is drawn
inside a square ABCD. What is the value of the angle APD in degrees?
A. 75
B. 90
C. 120
D. 135
E. 150
