Page 1 Page 1 Proctored Mock CAT10 2012 Section I 1. a 1 , a 2 , a 3 , a 4 , …, a 31 are in arithmetic progression. If a 1 + a 7 + a 13 + a 19 + a 25 + a 31 = 372, find the value of a 16 . (a) 60 (b) 62 (c) 64 (d) 66 2. In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and PTQ 90 , ?=° what is the area (in cm 2 ) of the rectangle PQRS? P Q S T R 16 cm 24 cm (a) 384 (b) 192 (c) 768 (d) None of these 3. Two trains T1 and T2 start from stations A and B towards each other at speeds of 50 km/hr and 30 km/hr respectively. When they meet, it is found that the slower train has travelled 24 km less than the faster train. What is the distance (in km) between the two stations A and B? (a) 216 (b) 146 (c) 120 (d) 96 4. A survey was conducted on a group of people comprising 60% men and 40% women. Among men, 1 16 were married. Among women, 30% were married and 25% of the married women were housewives. If 70% people in the group were married, what was the number of married working women? (a) 18 (b) 24 (c) 28 (d) 20 5. The length (in metres) of the diagonals of three adjacent faces of a cuboidal room are 213,4 5 and 10. What is half the length (in metres) of the largest possible straight rod that can be placed in the room? (a) 229 (b) 258 (c) 29 (d) 58 Proctored Mock CAT 10 2012 Page 2 Page 1 Proctored Mock CAT10 2012 Section I 1. a 1 , a 2 , a 3 , a 4 , …, a 31 are in arithmetic progression. If a 1 + a 7 + a 13 + a 19 + a 25 + a 31 = 372, find the value of a 16 . (a) 60 (b) 62 (c) 64 (d) 66 2. In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and PTQ 90 , ?=° what is the area (in cm 2 ) of the rectangle PQRS? P Q S T R 16 cm 24 cm (a) 384 (b) 192 (c) 768 (d) None of these 3. Two trains T1 and T2 start from stations A and B towards each other at speeds of 50 km/hr and 30 km/hr respectively. When they meet, it is found that the slower train has travelled 24 km less than the faster train. What is the distance (in km) between the two stations A and B? (a) 216 (b) 146 (c) 120 (d) 96 4. A survey was conducted on a group of people comprising 60% men and 40% women. Among men, 1 16 were married. Among women, 30% were married and 25% of the married women were housewives. If 70% people in the group were married, what was the number of married working women? (a) 18 (b) 24 (c) 28 (d) 20 5. The length (in metres) of the diagonals of three adjacent faces of a cuboidal room are 213,4 5 and 10. What is half the length (in metres) of the largest possible straight rod that can be placed in the room? (a) 229 (b) 258 (c) 29 (d) 58 Proctored Mock CAT 10 2012 Page 2 Proctored Mock CAT10 2012 Directions for questions 6 to 8: Answer the questions on the basis of the information given below. Pie ChartI shows the percentage breakup of the 2.90 million tonnes of tea produced by six countries in the year 2010. Pie ChartII shows the breakup of the total revenue of $8380 million generated by selling 2.90 million tonnes of tea produced by these countries in the year. Pie Chart – I China 35% India 30% Sri Lanka 11% Kenya 12% Turkey 7% Indonesia 5% Pie Chart – II China 28% India 36% Sri Lanka 13% Kenya 9% Turkey 8% Indonesia 6% 6. By what percent is the revenue generated per tonne of tea produced by Kenya more/less than that of Indonesia? (a) 60 (b) 42.5 (c) 37.5 (d) 31.4 7. What is the approximate difference between the revenue generated (in $ per kg) of tea produced by India and China? (a) 1.156 (b) 0.867 (c) 1.011 (d) 1.445 8. If the revenue generated per tonne of tea produced by China, Turkey and Sri Lanka are represented by C, T and S respectively, which of the following is true? (a) T > S > C (b) S > T > C (c) S > C > T (d) C > T > S 9. If one of the roots of the equation 2x 2 + (3k + 4)x + (9k 2 – 3k – 1) = 0 is twice the other, then which of the following can be a value of ‘k’? (a) 2 3  (b) 2 3 (c) 1 3  (d) 1 3 10. A line x + y = 14 cuts the curve y = x 2 + 4x at two distinct points. What type of triangle will be formed by joining these two points to a third point (1, 20)? (a) Equilateral (b) Isosceles (c) Scalene (d) No such triangle is possible Page 3 Page 1 Proctored Mock CAT10 2012 Section I 1. a 1 , a 2 , a 3 , a 4 , …, a 31 are in arithmetic progression. If a 1 + a 7 + a 13 + a 19 + a 25 + a 31 = 372, find the value of a 16 . (a) 60 (b) 62 (c) 64 (d) 66 2. In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and PTQ 90 , ?=° what is the area (in cm 2 ) of the rectangle PQRS? P Q S T R 16 cm 24 cm (a) 384 (b) 192 (c) 768 (d) None of these 3. Two trains T1 and T2 start from stations A and B towards each other at speeds of 50 km/hr and 30 km/hr respectively. When they meet, it is found that the slower train has travelled 24 km less than the faster train. What is the distance (in km) between the two stations A and B? (a) 216 (b) 146 (c) 120 (d) 96 4. A survey was conducted on a group of people comprising 60% men and 40% women. Among men, 1 16 were married. Among women, 30% were married and 25% of the married women were housewives. If 70% people in the group were married, what was the number of married working women? (a) 18 (b) 24 (c) 28 (d) 20 5. The length (in metres) of the diagonals of three adjacent faces of a cuboidal room are 213,4 5 and 10. What is half the length (in metres) of the largest possible straight rod that can be placed in the room? (a) 229 (b) 258 (c) 29 (d) 58 Proctored Mock CAT 10 2012 Page 2 Proctored Mock CAT10 2012 Directions for questions 6 to 8: Answer the questions on the basis of the information given below. Pie ChartI shows the percentage breakup of the 2.90 million tonnes of tea produced by six countries in the year 2010. Pie ChartII shows the breakup of the total revenue of $8380 million generated by selling 2.90 million tonnes of tea produced by these countries in the year. Pie Chart – I China 35% India 30% Sri Lanka 11% Kenya 12% Turkey 7% Indonesia 5% Pie Chart – II China 28% India 36% Sri Lanka 13% Kenya 9% Turkey 8% Indonesia 6% 6. By what percent is the revenue generated per tonne of tea produced by Kenya more/less than that of Indonesia? (a) 60 (b) 42.5 (c) 37.5 (d) 31.4 7. What is the approximate difference between the revenue generated (in $ per kg) of tea produced by India and China? (a) 1.156 (b) 0.867 (c) 1.011 (d) 1.445 8. If the revenue generated per tonne of tea produced by China, Turkey and Sri Lanka are represented by C, T and S respectively, which of the following is true? (a) T > S > C (b) S > T > C (c) S > C > T (d) C > T > S 9. If one of the roots of the equation 2x 2 + (3k + 4)x + (9k 2 – 3k – 1) = 0 is twice the other, then which of the following can be a value of ‘k’? (a) 2 3  (b) 2 3 (c) 1 3  (d) 1 3 10. A line x + y = 14 cuts the curve y = x 2 + 4x at two distinct points. What type of triangle will be formed by joining these two points to a third point (1, 20)? (a) Equilateral (b) Isosceles (c) Scalene (d) No such triangle is possible Page 3 Proctored Mock CAT10 2012 11. N = 2.xxyxxyxxy…, where at most one of the digits x and y is 0. Which of the following numbers, when multiplied by N, necessarily results in an integer? (a) 198 (b) 666 (c) 990 (d) 1998 12. The speed of a railway engine is 45 kmph when no bogie is attached to it. It is observed that the reduction in the speed of the engine is directly proportional to the square root of the number of bogies attached to it. If the speed of the train is 9 kmph when 16 bogies are attached, find the maximum number of bogies that can be carried by the engine. (a) 25 (b) 24 (c) 23 (d) 22 13. The question given below is followed by two statements, A and B. Mark the answer using the following instructions: Mark (a) if the question can be answered by using both the statements together, but cannot be answered using either statement alone. Mark (b) if the question can be answered by using either statement alone. Mark (c) if the question cannot be answered even by using both the statements together. Mark (d) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone. Q. In how many days can 16 men and 4 women do a job? A. A woman is 80% as efficient as a man. B. Four men work for 8 days on the job. Then seven women work for 4 days to finish the remaining part of the job. 14. A circle cuts a square at 8 distinct points such that each side of the square contains a chord of the circle equal to the length of the radius of the circle. Find the ratio of the area of the circle to that of the square. (a) :3 p (b) :3 p (c) :2 p (d) 2:3 p 15. What is the unit digit of + 21 25 14 15 74? (a) 3 (b) 5 (c) 7 (d) 9 16. () ?? + = ? ??  ?? 3 1 f x 4 2f x , where x 4. x4 Find the value of f(2). (a) 45 4  (b) 25 6  (c) 45 7  (d) 25 6 Page 4 Page 1 Proctored Mock CAT10 2012 Section I 1. a 1 , a 2 , a 3 , a 4 , …, a 31 are in arithmetic progression. If a 1 + a 7 + a 13 + a 19 + a 25 + a 31 = 372, find the value of a 16 . (a) 60 (b) 62 (c) 64 (d) 66 2. In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and PTQ 90 , ?=° what is the area (in cm 2 ) of the rectangle PQRS? P Q S T R 16 cm 24 cm (a) 384 (b) 192 (c) 768 (d) None of these 3. Two trains T1 and T2 start from stations A and B towards each other at speeds of 50 km/hr and 30 km/hr respectively. When they meet, it is found that the slower train has travelled 24 km less than the faster train. What is the distance (in km) between the two stations A and B? (a) 216 (b) 146 (c) 120 (d) 96 4. A survey was conducted on a group of people comprising 60% men and 40% women. Among men, 1 16 were married. Among women, 30% were married and 25% of the married women were housewives. If 70% people in the group were married, what was the number of married working women? (a) 18 (b) 24 (c) 28 (d) 20 5. The length (in metres) of the diagonals of three adjacent faces of a cuboidal room are 213,4 5 and 10. What is half the length (in metres) of the largest possible straight rod that can be placed in the room? (a) 229 (b) 258 (c) 29 (d) 58 Proctored Mock CAT 10 2012 Page 2 Proctored Mock CAT10 2012 Directions for questions 6 to 8: Answer the questions on the basis of the information given below. Pie ChartI shows the percentage breakup of the 2.90 million tonnes of tea produced by six countries in the year 2010. Pie ChartII shows the breakup of the total revenue of $8380 million generated by selling 2.90 million tonnes of tea produced by these countries in the year. Pie Chart – I China 35% India 30% Sri Lanka 11% Kenya 12% Turkey 7% Indonesia 5% Pie Chart – II China 28% India 36% Sri Lanka 13% Kenya 9% Turkey 8% Indonesia 6% 6. By what percent is the revenue generated per tonne of tea produced by Kenya more/less than that of Indonesia? (a) 60 (b) 42.5 (c) 37.5 (d) 31.4 7. What is the approximate difference between the revenue generated (in $ per kg) of tea produced by India and China? (a) 1.156 (b) 0.867 (c) 1.011 (d) 1.445 8. If the revenue generated per tonne of tea produced by China, Turkey and Sri Lanka are represented by C, T and S respectively, which of the following is true? (a) T > S > C (b) S > T > C (c) S > C > T (d) C > T > S 9. If one of the roots of the equation 2x 2 + (3k + 4)x + (9k 2 – 3k – 1) = 0 is twice the other, then which of the following can be a value of ‘k’? (a) 2 3  (b) 2 3 (c) 1 3  (d) 1 3 10. A line x + y = 14 cuts the curve y = x 2 + 4x at two distinct points. What type of triangle will be formed by joining these two points to a third point (1, 20)? (a) Equilateral (b) Isosceles (c) Scalene (d) No such triangle is possible Page 3 Proctored Mock CAT10 2012 11. N = 2.xxyxxyxxy…, where at most one of the digits x and y is 0. Which of the following numbers, when multiplied by N, necessarily results in an integer? (a) 198 (b) 666 (c) 990 (d) 1998 12. The speed of a railway engine is 45 kmph when no bogie is attached to it. It is observed that the reduction in the speed of the engine is directly proportional to the square root of the number of bogies attached to it. If the speed of the train is 9 kmph when 16 bogies are attached, find the maximum number of bogies that can be carried by the engine. (a) 25 (b) 24 (c) 23 (d) 22 13. The question given below is followed by two statements, A and B. Mark the answer using the following instructions: Mark (a) if the question can be answered by using both the statements together, but cannot be answered using either statement alone. Mark (b) if the question can be answered by using either statement alone. Mark (c) if the question cannot be answered even by using both the statements together. Mark (d) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone. Q. In how many days can 16 men and 4 women do a job? A. A woman is 80% as efficient as a man. B. Four men work for 8 days on the job. Then seven women work for 4 days to finish the remaining part of the job. 14. A circle cuts a square at 8 distinct points such that each side of the square contains a chord of the circle equal to the length of the radius of the circle. Find the ratio of the area of the circle to that of the square. (a) :3 p (b) :3 p (c) :2 p (d) 2:3 p 15. What is the unit digit of + 21 25 14 15 74? (a) 3 (b) 5 (c) 7 (d) 9 16. () ?? + = ? ??  ?? 3 1 f x 4 2f x , where x 4. x4 Find the value of f(2). (a) 45 4  (b) 25 6  (c) 45 7  (d) 25 6 Page 4 Proctored Mock CAT10 2012 Directions for questions 17 to 19: Answer the questions on the basis of the information given below. A group of 25 students from various graduation and post graduation courses across four renowned colleges took a Common Analytical Exam in which they were scored out of 100. The table given below shows the breakup of the number of students across graduation and post graduation and also the highest and the lowest scores in each group. Graduation Post Graduation College Highest score Lowest score No. of students Highest score Lowest score No. of students Total AMS 80 78 2 79 65 4 6 PCL 92 56 4 84 84 1 5 NDMM 96 61 7 90 90 1 8 JIME 85 84 3 89 68 3 6 Total 16 9 25 17. At least what percentage of the students in the group scored below 80? (a) 16% (b) 32% (c) 16.67% (d) 28.11% 18. At most how many students of the group scored more than 72? (a) 17 (b) 19 (c) 20 (d) 21 19. What is the absolute difference between the maximum and the minimum number of students scoring in the range 66 to 84 (both inclusive)? (a) 11 (b) 13 (c) 15 (d) 12 20. How many natural numbers are factors of at least one of 6 14 , 10 12 and 15 20 ? (a) 835 (b) 834 (c) 794 (d) 795 21. Avnish counted the digits used to number the pages of a book and found that the total number of digits used was 3441. Find the number of pages in the book. (a) 1128 (b) 1137 (c) 1413 (d) None of these 22. Mr. X sold two books, one at a loss of 11.11% and the other at a gain of 25%. If the two books had cost him the same, what was his approximate overall gain/loss? (a) 7% loss (b) 9% gain (c) 6% gain (d) 7% gain 23. ABCD is a cyclic isosceles trapezium where AD and BC are the two parallel sides and the lengths of the sides AB, AD and BC are in the ratio 4 : 4 : 5. What is the ratio AD : AC? (a) 2 : 5 (b) 2 : 3 (c) 4 : 5 (d) 4 : 7 24. If log x n is the average of n and log x log x n, which of the following best describes ‘n’ for x = 10? (a) 0 < n < 1 (b) 1 < n < 10 (c) 10 < n < 100 (d) 100 < n < 1000 Page 5 Page 1 Proctored Mock CAT10 2012 Section I 1. a 1 , a 2 , a 3 , a 4 , …, a 31 are in arithmetic progression. If a 1 + a 7 + a 13 + a 19 + a 25 + a 31 = 372, find the value of a 16 . (a) 60 (b) 62 (c) 64 (d) 66 2. In the figure given below, PQRS is a rectangle. If PT = 16 cm, QT = 24 cm and PTQ 90 , ?=° what is the area (in cm 2 ) of the rectangle PQRS? P Q S T R 16 cm 24 cm (a) 384 (b) 192 (c) 768 (d) None of these 3. Two trains T1 and T2 start from stations A and B towards each other at speeds of 50 km/hr and 30 km/hr respectively. When they meet, it is found that the slower train has travelled 24 km less than the faster train. What is the distance (in km) between the two stations A and B? (a) 216 (b) 146 (c) 120 (d) 96 4. A survey was conducted on a group of people comprising 60% men and 40% women. Among men, 1 16 were married. Among women, 30% were married and 25% of the married women were housewives. If 70% people in the group were married, what was the number of married working women? (a) 18 (b) 24 (c) 28 (d) 20 5. The length (in metres) of the diagonals of three adjacent faces of a cuboidal room are 213,4 5 and 10. What is half the length (in metres) of the largest possible straight rod that can be placed in the room? (a) 229 (b) 258 (c) 29 (d) 58 Proctored Mock CAT 10 2012 Page 2 Proctored Mock CAT10 2012 Directions for questions 6 to 8: Answer the questions on the basis of the information given below. Pie ChartI shows the percentage breakup of the 2.90 million tonnes of tea produced by six countries in the year 2010. Pie ChartII shows the breakup of the total revenue of $8380 million generated by selling 2.90 million tonnes of tea produced by these countries in the year. Pie Chart – I China 35% India 30% Sri Lanka 11% Kenya 12% Turkey 7% Indonesia 5% Pie Chart – II China 28% India 36% Sri Lanka 13% Kenya 9% Turkey 8% Indonesia 6% 6. By what percent is the revenue generated per tonne of tea produced by Kenya more/less than that of Indonesia? (a) 60 (b) 42.5 (c) 37.5 (d) 31.4 7. What is the approximate difference between the revenue generated (in $ per kg) of tea produced by India and China? (a) 1.156 (b) 0.867 (c) 1.011 (d) 1.445 8. If the revenue generated per tonne of tea produced by China, Turkey and Sri Lanka are represented by C, T and S respectively, which of the following is true? (a) T > S > C (b) S > T > C (c) S > C > T (d) C > T > S 9. If one of the roots of the equation 2x 2 + (3k + 4)x + (9k 2 – 3k – 1) = 0 is twice the other, then which of the following can be a value of ‘k’? (a) 2 3  (b) 2 3 (c) 1 3  (d) 1 3 10. A line x + y = 14 cuts the curve y = x 2 + 4x at two distinct points. What type of triangle will be formed by joining these two points to a third point (1, 20)? (a) Equilateral (b) Isosceles (c) Scalene (d) No such triangle is possible Page 3 Proctored Mock CAT10 2012 11. N = 2.xxyxxyxxy…, where at most one of the digits x and y is 0. Which of the following numbers, when multiplied by N, necessarily results in an integer? (a) 198 (b) 666 (c) 990 (d) 1998 12. The speed of a railway engine is 45 kmph when no bogie is attached to it. It is observed that the reduction in the speed of the engine is directly proportional to the square root of the number of bogies attached to it. If the speed of the train is 9 kmph when 16 bogies are attached, find the maximum number of bogies that can be carried by the engine. (a) 25 (b) 24 (c) 23 (d) 22 13. The question given below is followed by two statements, A and B. Mark the answer using the following instructions: Mark (a) if the question can be answered by using both the statements together, but cannot be answered using either statement alone. Mark (b) if the question can be answered by using either statement alone. Mark (c) if the question cannot be answered even by using both the statements together. Mark (d) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone. Q. In how many days can 16 men and 4 women do a job? A. A woman is 80% as efficient as a man. B. Four men work for 8 days on the job. Then seven women work for 4 days to finish the remaining part of the job. 14. A circle cuts a square at 8 distinct points such that each side of the square contains a chord of the circle equal to the length of the radius of the circle. Find the ratio of the area of the circle to that of the square. (a) :3 p (b) :3 p (c) :2 p (d) 2:3 p 15. What is the unit digit of + 21 25 14 15 74? (a) 3 (b) 5 (c) 7 (d) 9 16. () ?? + = ? ??  ?? 3 1 f x 4 2f x , where x 4. x4 Find the value of f(2). (a) 45 4  (b) 25 6  (c) 45 7  (d) 25 6 Page 4 Proctored Mock CAT10 2012 Directions for questions 17 to 19: Answer the questions on the basis of the information given below. A group of 25 students from various graduation and post graduation courses across four renowned colleges took a Common Analytical Exam in which they were scored out of 100. The table given below shows the breakup of the number of students across graduation and post graduation and also the highest and the lowest scores in each group. Graduation Post Graduation College Highest score Lowest score No. of students Highest score Lowest score No. of students Total AMS 80 78 2 79 65 4 6 PCL 92 56 4 84 84 1 5 NDMM 96 61 7 90 90 1 8 JIME 85 84 3 89 68 3 6 Total 16 9 25 17. At least what percentage of the students in the group scored below 80? (a) 16% (b) 32% (c) 16.67% (d) 28.11% 18. At most how many students of the group scored more than 72? (a) 17 (b) 19 (c) 20 (d) 21 19. What is the absolute difference between the maximum and the minimum number of students scoring in the range 66 to 84 (both inclusive)? (a) 11 (b) 13 (c) 15 (d) 12 20. How many natural numbers are factors of at least one of 6 14 , 10 12 and 15 20 ? (a) 835 (b) 834 (c) 794 (d) 795 21. Avnish counted the digits used to number the pages of a book and found that the total number of digits used was 3441. Find the number of pages in the book. (a) 1128 (b) 1137 (c) 1413 (d) None of these 22. Mr. X sold two books, one at a loss of 11.11% and the other at a gain of 25%. If the two books had cost him the same, what was his approximate overall gain/loss? (a) 7% loss (b) 9% gain (c) 6% gain (d) 7% gain 23. ABCD is a cyclic isosceles trapezium where AD and BC are the two parallel sides and the lengths of the sides AB, AD and BC are in the ratio 4 : 4 : 5. What is the ratio AD : AC? (a) 2 : 5 (b) 2 : 3 (c) 4 : 5 (d) 4 : 7 24. If log x n is the average of n and log x log x n, which of the following best describes ‘n’ for x = 10? (a) 0 < n < 1 (b) 1 < n < 10 (c) 10 < n < 100 (d) 100 < n < 1000 Page 5 Proctored Mock CAT10 2012 25. Find the value of 4 . 25 1 10 1 52 1 52  +  + +  (a) 45  (b) 8 (c) 55 + (d) None of these 26. A table of ‘n’ rows and ‘n’ columns is created such that the value of the cell in the i th row and the j th column is given by (i + 1) + j. Some numbers are selected from the table. If it is found that exactly one number has been selected from each row and each column, then the sum of the selected numbers will be equal to (a) n 2 + 1 (b) () nn 1 2 + (c) n(n + 2) (d) n(n + 1) 27. From the first ‘n’ consecutive natural numbers written on a blackboard, one of the numbers is removed. If the average of the remaining numbers is 2 32 , 9 then find the number removed. (a) 50 (b) 64 (c) 46 (d) None of these Directions for questions 28 to 30: Answer the questions on the basis of the information given below. A company employs two different processes in its production wing. Both the processes require an initial investment of 5 lakh each. The bar graph given below shows the running cost for both the production processes. The running cost (in ) for both the processes comprises the maintenance cost, the material cost and the labour cost. The production happens in shifts and one shift is of six hours. Even if the target production is achieved before the end of a shift, the company has to bear the complete maintenance cost and the labour cost for that shift. 500 250 500 330 150 501 0 200 400 600 800 1000 1200 Maintenance cost per shift Material cost per 1000 units Labour cost per shift Process1 Process2Read More
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