CAT2006 Related Question Answers

1. 2. 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 that remains after punching is:

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

4. What is the weight of Praja’s luggage?

5. What is the free luggage allowance?

6. If x = -0.5, then which of the following has the smallest value?

7. Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?

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

9. 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

10. Consider a sequence where the $$n^{th}$$ term, $$t_n = n/(n+2), n =1, 2, ....$$ The value of $$t_3 * t_4 * t_5 * …..* t_{53}$$ equals.

11. 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?

12. What are the values of x and y that satisfy both the equations?$$2^{0.7x} * 3^{-1.25y} = 8\sqrt{6}/27$$$$4^{0.3x} * 9^{0.2y} = 8*81^{1/5}$$

13. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x

14. 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:Only September: 18;September but not August: 23;September and July: 8;September:28;July: 48;July and August: 10;none of the three months: 24What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

15. 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?

16. The graph of y - x (on the y axis) against y + x (on the x axis) is as shown below. (All graphs in this question are drawn to scale and the same scale and the same scale has been used on each axis.)Which of the following shows the graph of y against x?

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

18. What values of x satisfy $$x^{2/3} + x^{1/3} - 2

19. Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:

20. 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?

21. 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?

22. 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:

23. 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?[CAT 2006]

24. 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:

25. If $$log_y x = (alog_z y) = (blog_x z) = ab$$, then which of the following pairs of values for (a, b) is not possible?

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CAT2006 Related Question Answers

1.

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

4. What is the weight of Praja’s luggage?

5. What is the free luggage allowance?

6. If x = -0.5, then which of the following has the smallest value?

7. Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?

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

9. 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

10. Consider a sequence where the $$n^{th}$$ term, $$t_n = n/(n+2), n =1, 2, ....$$ The value of $$t_3 * t_4 * t_5 * …..* t_{53}$$ equals.

11. 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?

12. What are the values of x and y that satisfy both the equations?$$2^{0.7x} * 3^{-1.25y} = 8\sqrt{6}/27$$$$4^{0.3x} * 9^{0.2y} = 8*81^{1/5}$$

13. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x

15. 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?

16. The graph of y - x (on the y axis) against y + x (on the x axis) is as shown below. (All graphs in this question are drawn to scale and the same scale and the same scale has been used on each axis.)Which of the following shows the graph of y against x?

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

18. What values of x satisfy $$x^{2/3} + x^{1/3} - 2

19. Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:

20. 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?

21. 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?

22. 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:

23. 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?[CAT 2006]

24. 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:

25. If $$log_y x = (a*log_z y) = (b*log_x z) = ab$$, then which of the following pairs of values for (a, b) is not possible?

25. If $$log_y x = (alog_z y) = (blog_x z) = ab$$, then which of the following pairs of values for (a, b) is not possible?