|CAT 2k passage 1|
|CAT 2k passage 2|
|CAT 2000 passage 3 Test|
|CAT 2000 passage 4 Test|
|CAT 2000 passage 5 Test|
- If two of the sides of a right angled triangle are 10 cm and 10.5 cm and its inradius is 3 cm, what is its circumradius?
a. 14.5 cm b. 7.25 cm c. 5.25 cm d. 5 cm
2. Mehras have a large family. Ravi Mehra has thrice as many brothers as sisters and his sister Beenu has four times as many brothers as sisters. How many brothers does Ravi have?
a. 12 b. 11 c. 15 d. 16
3. Given that a, b, c are in continued proportion and b, c, d are also in continued proportion, if b : c = 2 : 3 and all the four numbers are positive integers, what is the minimum possible value of (a + d)?
a. 35 b. 97 c. 13 d. 65
4. A quadrilateral ABCD is circumscribed about a circle. If AB = 10 cm, BC = 12 cm, CD = 9 cm, then find AD.
a. 6 cm b. 7 cm c. 8 cm d. CBD
5. At 7:00 am, Anil started from P towards Q and Bhanu started from Q towards P. At 9:00 am, they crossed each other and continued towards their respective destinations. If the total time taken by Anil to reach his destination is three hours more than taken by Bhanu, what is the ratio of Anil’s speed to Bhanu’s speed?
a. 1 : 2 b. 2 : 5 c. 2 : 3 d. CBD
7. A group of men can complete a job in M hours. But after every 8 hours, half the numbers of men working at that point of time leave the job. Continuing this way, if the job is finished in 40 hours, what is the value of M?
a. 15 b. 61/4 c. 63/4 d. 31/2
8. A natural number n is such that 120 ≤ n ≤ 240. If HCF of n and 240 is 1, how many values of n are possible?
a. 24 b. 32 c. 36 d. 40
9. In a certain school, class X students are x % of the total strength of the school. If 10 students join class X, then class X students will become (x + 9) % of the total strength of the school. Which of the following can be the initial total strength of the school? Assume that there is no change in the number of students in the other classes.
a. 91 b. 40 c. 60 d. 70
10. The ratio of the ages of A and B twelve years ago was 2: 3 and the ratio of the ages of B and C 12 years from now will also be 2 : 3.If the average age of A and C at present is 57 years, the ratio of the ages of B and C was/will be 1: 2
a. 6 years ago b. 12 years ago c. 18 years ago d. 18 years from now
11. When the weight of a new person is included, the average weight of the group increases by 1 kg. Instead, if the new person replaces one of the persons in the group, the average weight of the group decreases by 1 kg. If the weight of the replaced person is 50 kg, which of the following statements are definitely true?
- Twice the weight of the new person is more than the original average weight of the group.
- The original number of members in the group is odd.
- The magnitude, in kg, of the weight of the new person is an odd number.
- The magnitude, in kg, of the original average weight of the group is an odd number.
a. only B and D b. Only B and C c. Only A and D d. Only A and C
12. P started running around a circular track, of length 800 m from the starting point A. When P reaches the 600 m mark, Q started running around the track from A in the same direction as P. When Q reached the 400 m mark, R started from A in the same direction as Q. When R reached the 200 m mark, S started from A in the same direction as R. When P reached A for the first time, Q, R and S also reached A, for the first time. What is the ratio of speeds of P,Q, R and S?
a. 1 : 2 : 3 : 4 b. 1 : 4 : 8 : 16 c. 3 : 12 : 24 : 32 d. 1 : 4 : 16 : 64
13. Five friends A1, A2, A3, A4 and A5 take up an assignment. It is known that, for i = 1 to 4, Ai, when working alone, takes (i + 1) times as much time as the other four would take, when working together. If all the five friends work together on the assignment and they earn a total of Rs 600, what is the share of A5?
a. Rs 40 b. Rs 20 c. Rs 25 d. Rs 30
14. What is the hundreds digit of 10! + 11! + 12! +…………….+ 100!?
a. 2 b. 3 c. 6 d. 8
18. If the sum of the number of zeros in the factorials of each of the first n natural numbers is 250, the factorials of how many of these natural numbers will end with an odd number of zeros?
a. 20 b. 22 c. 23 d. 25
19. For a regular polygon of n sides, if the ratio of the external angle to the internal angle is an integer, then find the number of possible values of n.
a. 1 b. 2 c. 4 d. more than 4
20. A and B, working together, can build a wall, 221 m long in 100/9 days. If they work on alternate days, with A starting the work, it takes 89/4 days to build the same wall. If A and B work together and build a similar wall but of twice the length and earn a total of Rs 1800 for it, then B’s share of earnings is
a. Rs 750 b. Rs 800 c. Rs 1000 d. Rs 1050
21. N is the least natural number which when divided by k, k + 1, k + 2 successively, where k is a natural number, leaves a remainder of (k – 1), k, (k + 1) respectively. Which of the following is not a possible value of N?
a. 59 b. 119 c. 11 d. 23
22. If x0 = 1 and xn+1 + 12n = 5xn + 3, find x200.
a. 5200 – 600 b. 5200 + 600 c. 5199 – 600 d. 5199 + 600
- A ten digit number N is divisible by both 72 and 88. If N = x123y4566z, then how many distinct values of N are possible?
a. 1 b. 5 c. 10 d. 6 e. 4
2. A pentagon ABCDE is inscribed in a circle. From a point P outside the circle, two tangents, which touch the circle at B and C respectively, are drawn. If angle BCA is 36 degrees and angle AEC = 78 degrees, then find angle BPC (in degrees).
a. 96 b. 78 c. 102 d. 84 e. 114
4. Two boys Ajay and Bijay start simultaneously from P towards Q. At the same time another boy, Chatur, started from Q towards P. After Bijay traveled exactly one-third of the distance PQ, both Ajay and Bijay reversed their direction (but maintained their respective speeds) and traveled towards P, while chatur continued in his initial direction and met exactly at P. Which of the following ratios can be found using the information given?
- Ratio of speeds of Ajay and Bijay
- Ratio of speeds of Bijay and chatur.
- Ratio of speeds of Chatur and Ajay
a. Only I b. Only II c. Only III d. I, II and III e. None of I,II and III
5. A tap takes 8 seconds to fill a jar and 6 minutes to fill a drum. Ram has to fill the drum with the jar. First he fills the jar and then brings it to the drum and pours the water into the drum. The time taken to bring the jar from the tap to the drum is 10 seconds. Unfortunately, the jar develops a leak, which can empty the full jar in 40 seconds. What will be the minimum total time required by Ram to fill the drum?
a. 75/4 mins b. 18 mins c. 20 mins d. 16.66 mins e. 12 mins
Instructions for question no.6 to 8: Read the following instructions given below.
In a management entrance test there are 150 questions. Six marks are awarded for each correct answer, two marks are deducted for each wrong answer and one mark is deducted for each question left unattempted.
6. A candidate gets a net score of 420. If he got as many wrong answers as the number of questions he left unattempted, how many questions did he answer correctly?
a. 86 b. 84 c. 70 d. 80
7. Which of the following could be the number of questions left unattempted by a candidate who gets a net score of 360?
a. 24 b. 26 c. 28 d. 30
8. What is the total number of distinct scores that are possible, if a candidate attempts all the questions?
a. 150 b. 151 c. 1200 d. 1201
9. Shyam constructs a certain wall, working in a special way, and takes 12 days to complete it. If Ln is the length of the wall (in metres) that he constructs on the nth day, then
Ln = 2n, 0 ≤ n ≤ 4
= 8, for n =5
= 3n – 7, 6≤ n ≤ 12
Find the total length of the wall that he constructs in the first 10 days.
a. 31 m b. 35 m c. 93 m d. 113 m
10. 16 students were writing a test in a class. Sara, one of the students made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?
- At least two students made the same number of mistakes
- Exactly two students made the same number of mistakes.
- At most two students made the same number of mistakes.
- All students made different number of mistakes.
11. A function f(x) is defined for a real variable x, as f(x) = min(2 + 3x , 21 – 5x). The maximum possible value of f(x) is
a. 73/8 b. 19/8 c. 23/9 d. 53/9
12. Coffee beans of two different qualities are mixed and sold at 20 % profit. If the higher quality beans are sold at the above price, then the loss is 4 %. If the ratio of lower quality and the higher quality beans in the mixture is 5 : 2, then what is the % profit when the lower quality beans are sold at the same price?
a. 29.6 % b. 33.33 % c. 30 % d. none of these
13. I went to Sweet Chariot and found that there were three things to my liking – soft drinks costing Rs 11each, veg rolls costing Rs 7 each and veg cutlets costing Rs 8 each. I could have spent any amount between Rs 45 and Rs 50 (both values inclusive). In how many ways could I have purchased the items, if I wanted to purchase at least one of each of the items?
a. 4 b. 5 c. 6 d. 7
14. Rahul wanted to write down the squares of the first (2m + 1) whole numbers on a board but he missed exactly one of them, which happens to be the middle one. Sahil computed the average of these 2m numbers and found it to be less than 350. What could be the greatest value of m?
a. 15 b. 16 c. 17 d. none of these
15. How many three digit numbers satisfy all the following conditions?
- When divided by 4 or 3, they leave a remainder of 1 in each case.
- When divided by 56 and 32, they leave remainders of 49 and 25 respectively.
- When divided by 11 and 13, they leave remainders of 8 and 9 respectively.
a. 0 b. 1 c. 2 d. 3
16. The quadratic equations (2p – 1)x2 + (2p + 1)x + c = 0 and (q + 1)y2 + (4q + 1)y + 3c = 0 have the same pair of roots. Given that c ≠ 0, what is the value of (p + q)?
a. 3 b. 4 c. 6 d. CBD
17. The perimeter of an equilateral triangle equals the perimeter of a rectangle. If one of the sides of the rectangle equals the side of the triangle, find the ratio of the areas of the triangle and the rectangle.
a. √3 : 1 b. √3 : 2 c. 2√3 : 1 d. 2 : √3
18. The income of A is Rs 15000 and it is equal to the expenditure of B. If the ratio of the savings of A to the savings of B is 2 : 1, which of the following statements is definitely true?
a. The combined income of A and B is more than Rs 45000.
b. The combined expenditure of A and B is not less than Rs 20,000.
c. A’s expenditure added to twice of B’s income is equal to Rs 45000.
d. B’s expenditure added to twice of A’s income is equal to Rs 30000
19. A, B and C started a job. On the first day, C being unwell is not able to work at his full capacity and he leaves after one day. The other two complete the work and B gets a share of Rs 5100 out of a total of Rs 18000 paid for the job. If each of A, B and C can complete the job normally in 10 days, 20 days and 5 days respectively, find the % efficiency with which C worked on the first day.
a. 50 % b. 60 % c. 75 % d. 80 %
23. What is the remainder when (2469 + 3268) is divided by 22?
a. 1 b. 11 c. 19 d. 0
24. If x > 0, y > 0 and z > 0 and 12xyz = 108, find the minimum value of 2x + 3y + 4z.
a. 12 b. 18 c. 24 d. 27
25. Let Sn be defined as Sn = t0 + t1 + t2 ………..+ tn-1 + tn, where tn = (–1)n+1(tn-1 + 1) and t0 = 1. Find S199.
a. – 100 b. 100 c. – 99 d. – 199
Links to related theory
Section 1: Quantitative Aptitude & Data Interpretation
1. 2 2. 4 3. 1 4. 1 5. 2 6. 3 7. 3 8. 2 9. 2 10. 2
11. 4 12. 2 13. 3 14. 1 15. 4 16. 4 17. 4 18. 1 19. 5 20. 3 21. 2 22. 1 23. 4 24. 3 25. 3 26. 1
27. 2 28. 1 29. 1 30. 1
Section 2: Logical Reasoning & English Usage
31. 2 32. 1 33. 3 34. 4 35. 2 36. 4 37. 1 38. 4 39. 3 40. 2 41. 1
42. 1 43. 2 44. 4 45. 1 46. 5 47. 3 48. 4 49. 1 50. 3 51. 4
52. 3 53. 5 54. 1 55. 5 56. 2 57. 5 58. 1 59. 2 60. 3
This is most definitively positively compulsory for anybody who has completed these modules.
|Ratio Quiz 1||Immediate|
|Ratio Quiz 2||Immediate|
|Multipying factors quiz||Immediate|
|Percentages Quiz 1||Immediate|
|Percentage Quiz 2||Immediate|
|2||TSD proportionality quiz||Immediate|
|TSD relative speed basics||Immediate|
|TSD average speed||Immediate|