CAT 1997

Directions for Q 1 to 3: A race consists of three stretches A, B and C of 2 kms length each. The mode of coverage, and maximum and minimum of speeds possible in each stretch are:

 

Speed in a given stretch remains constant. The previous record was ten minutes to complete the race.

Q1. Anshuman travelled at the minimum speed by car and at maximum speed over the stretch B. What should be his minimum speed overstretch C to beat the previous record?

a. 15 kmph

b. Not possible to beat the previous record

c. 20 kmph

d. None of these

 

Q2. Mr. Hare travelled at the slowest speed in stretch A and took the same amount of time to travel in stretch B as he took in stretch A. If he took fifty percent more time than the previous record to complete the race, what was his speed in the stretch C?

a. 10 kmph

b. 15 km/h

c. 20 kmph

d. None of these

 

Q3. Mr. Tortoise travelled in the overall race at an average speed of 20 km/h. However, his average speed over the first two stretches combined was four times that over the last stretch. What was his speed over the last stretch?

a. 15 km/h

b. 10 km/h

c. 20 km/h

d. Cannot be determined

 

Directions for questions 4 to 6: There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.

Q4. What is the average weight of the students in group D?

a. More than the average weight of A

b. More than the average weight of C

c. Less than the average weight of C

d. Cannot be determined.

 

Q5. If one student from Group A is shifted to group B, which of the following will be true?

a. The average weight of both groups increases

b. The average weight of both the groups decreases

c. The average weight of the class remains the same

d. Cannot be determined

 

Q6. If all the students of the class have the same weight, then which of the following is false?

a. The average weight of all the four groups is the same

b. The total weight of A and C is twice the total weight of B

c. The average weight of D is greater than the average weight of A

d. The average weight of all the groups remains the same even if a number of students are shifted from one group to another

 

Directions Q 7 to 21:These questions are independent of each other

Q7. A student gets an aggregate of 60% marks in five subjects in the ratio 10:9:8:7:6. If the passing marks are 50% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?

a. 2

b. 3

c. 4

d. 5

 

Q8. In how many ways can the eight directors, the Vice chairman and the Chairman of a firm be seated at a round- table, if the Chairman has to sit between the Vice- chairman and a director?

a. 9!x2

b. 2×8!

c. 2×7!

d. None of these

 

Q9. If  , then what could be the value of x?

a. 3

b. 5

c. 4

d. None of these

 

Q10. After a discount of 11.1 1%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark his goods?

a. 28.56%

b. 35%

c. 22.22%

d. None of these

 

Q11. How many values of the natural number n are possible so that the expression is also a natural number?

a. Infinitely many

b. 3

c. 4

d. None of these

e. d & c

 

Q12. A dry fruit seller purchased 3 kinds of nuts at the rate of Rs. 100/kg, Rs. 80/kg and Rs.60/kg. He then mixed them, respectively, in the ratio 3:4:5 by weight and sold the same to a customer at 50% profit. The price at which he sold to the customer is

a. Rs. 110

b. Rs. 90

c. Rs. 70

d. None of these

 

Q13. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. The weight of dry grapes available from 20 kg of fresh grapes will be

a. 2 kg

b. 2.4 kg

c. 2.5 kg

d. None of these

 

Q14. An express train moving at the rate of 80 km per hour overtakes completely a good train twice as long and moving on a parallel line in the same direction at the rate of 40 km per hour in 54 seconds. How long will the express train take to completely pass through a station4000 meters in length?

a. 54 seconds

b. 27 seconds

c. 18 seconds

d. None of these

 

Q15. A candidate was asked to find 7/8th of a positive number; he found 7/18th of the same by mistake. If his answer was 770 less than the correct one, then the original given number was

a. 1260

b. 6160

c. 1584

d. None of these

 

Q16. P and Q are two integers such that PxQ = 64. Which of the following cannot be the value of P+Q?

a. 20

b. 65

c. 16

d. 35

 

Q17. The average marks of a student in ten papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

a. 55

b. 60

c. 62

d. Cannot be determined

 

Q18. If the roots, x1’ and x2’ of the quadratic equation also satisfy the equation 7×2 – 4×1 = 47 , then which of the following is true?

a. c = –15

b. x1 = -5, x2 = 3

c. x1 = 4.5, x2 = 2.5

d. None of these

 

Q19. The sum of the areas of two circles which touch each other externally is . If the sumof their radii is 15, find the ratio of the larger to the smaller radius.

a. 4

b. 2

c. 3

d. None of these

 

Q20. If m and n are integers divisible by 5, which of the following is not necessarily true?

a. m–n is divisibly 5

b. is divisible by 25

c. m+n is divisible by 10

d. None of the above

 

Q21. Which of the following is true?

d. None of these

 

Directions Q 22 to 24: A survey of 200 people in a community who watched at least one of the three channels – BBC, CNN and DD showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Q22. What is the maximum percent of people who can watch all the three channels?

a. 12.5

b. 8.5

c. 17

d. Insufficient data

 

Q23. If 5% of the people watched DD and CNN, 10% watched DD and BBC, then what percentof the people watched BBC and CNN only?

a. 2%

b. 5%

c. 8.5%

d. Cannot be determined

 

Q24. Referring to the previous question, how many percent of the people watched all the three channels?

a. 3.5%

b. 0%

c. 8.5%

d. Cannot be determined

 

Directions Q 25 to 27: These questions are independent of each other

Q25. A man earns x% on the first 2000 rupees and y% on the rest of his income. If he earns Rs700 from Rs 4000 and Rs 900 from Rs 5000 of income, find x

a. 20

b. 15

c. 35

d. None of these

 

Q26. AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD.

 

Q27. P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R

a. 5

b. 7

c. 9

d. 11

 

Directions Q 28 to 30: For these questions, the following functions have been defined:

la(x,y,z) = min(x+y, y+z)

le (x,y,z) = max(x–y, y–z)

ma(x,y,z)=(1/2) [le(x,y,z)+la(x,y,z)]

Q28. Given that x > y > z > 0, which of the following is necessarily true?

a. la(x,y,z) < le(x,y,z)

b. ma(x,y,z) < la(x,y,z)

c. ma(x,y,z) < le(x,y,z)

d. None of these

 

Q29. What is the value of ma(10, 4, le(la(10, 5, 3),5,3))

a. 7.0

b. 6.5

c. 8.0

d. 7.5

 

Q30. For x = 15, y = 10 and z = 9, find the value of:

le (x, min(y, x–z), le(9, 8, ma(x,y,z))

a. 5

b. 12

c. 9

d. 4

 

Directions Q 31 to 36: These questions are independent of each other.

Q31. ABC is a three-digit number in which A>O. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?

a. 9

b. 7

c. 4

d. 2

 

Q32. The adjoining figure shows a set of concentric squares.If the diagonal of the inner most square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh square, counting from the innermost square.

 

Q33. A, B and C are defined as follows:

Which of the following is true about the value of the above three expressions?

a. All of them lie between 0.18 and 0.20.

b. A is twice C.

c. C is the smallest.

d. B is the smallest

 

Q34. The value of each of a set of silver coins varies as the square of its diameter, if its thickness remains constant; and it varies as the thickness, if the diameter remains constant. If the diameters of two coins are in the ratio 4:3 what should the ratio of their thicknesses be if the value of the first is 4 times that of the second?

a. 16:9

b. 9:4

c. 9:16

d. 4:9

 

Q35. In a triangle ABC, points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq units, find the area of the triangle PQR

a. 10 sq. units

b. 15 sq. units

c. 5 sq. units

d. None of these

 

Q36. In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

a. 3:2b. 1:3

c. 2:5

d. 3:4

 

Directions Q 37and 38: At Weird Holiday Company, an employee gets a holiday on those days whose first letter is the same as the first letter of the employee’s name. All other days are working days. For instance, William gets a holiday on each Wednesday. Assume that the daily productivity of all employees is the same.

Q37. Raja stated the work on Sunday, the 25th February 1996 and finished the work on March 2, 1996. If  Tom and Jerry were assigned this task on 25th February 1996, when will the work have been completed?

a. 26th February 1996

b. 1St March 1996

c. 28th February 1996

d. Tom and Jerry cannot possibly work together

 

Q38. If Raja had actually completed the work on April 2, 1996, and if Tom and Shyam were assigned the same task on the same starting day, when will the work have been completed?

a. March 15, 1996

b. March 22,1996

c. March 29, 1996

d. April 2, 1996

 

Directions Q 39 to 41: Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 p.m. on Friday and reaches Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 a.m. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt.

Q39. If his journey, including stoppages, was covered at an average speed of 180 miles per hour, what was the distance between Frankfurt and India?

a. 3600 miles

b. 4500 miles

c. 5580 miles

d. Insufficient data

 

Q40. If X had started his return journey from India at 02:55 a.m. on the same day that he reached there, after how much time would he reach Frankfurt?

a. 24 hrs

b. 25 hrs

c. 26 hrs

d. Insufficient data

 

Q41. What was X’s average speed for the entire journey?

a. 170 mph

b. 180 mph

c. 165 mph

d. Insufficient data

 

Directions Q 42 to 43: These questions are independent of each other

Q42. In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC =12. What is the ratio of the area of the triangle CBE to that of the triangle ADE?

a. 1:4

b. 1:2

c. 1:3

d. Insufficient data

 

Q43. In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. AE = 22, BE = 6, CF = l6 and BF = 2. Find the length of the line joining the midpoints of the sides AB and BC.

b. 5

c. 3.5

d. None of these

 

Directions Q 44 and 45: These questions are based on the following data: A thief flees City A in a car towards City B on a stretch of straight road, 300 kilometers long, at the speed of 60 km/hr. In 15 minutes a police party (X) leaves city A to chase the thief at 65 km/hr.

Q44. After leaving how long does it take for the police party X to catch the thief’?

a. 2 hrs 45min

b. 3hrs

c. 3 hrs 15 min

d. None of these

 

Q45. If a police party (Y) were to leave City B at the same time as police party X leaving City A to catch the thief at 60km/hr., then which of the following statements is true?

a. Party X reaches 37.5 minutes after Party Y has caught the thief

b. Party Y reaches 37.5 minutes after Party X has caught the thie

c. Party X and Party Y has caught the thief together

d. Party X was 20 km away when the thief was caught

 

Directions Q 46 to 55: Data Sufficiency

Mark (a) If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark (b) If the question can be answered by using either statement alone.

Mark (c) If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Mark (d) If the question cannot be answered even by using both the statements together.

Q46. The values of x and y can be determined uniquely if

A. 3x + 2y=45

B. 10.5x + 7y=130

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

Q47. A number is divisible by 99 if

A. The number is simultaneously divisible by 9 and 11.

B. A number formed by reversing the positions of the digits of the same number is divisible by 99

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q48. The total capacity of production for two types of fans is 20,000 units. Using a total of 50 tons of materials for production of both types of fans and operating at full capacity, what is the production of the type I if

A. The rate of consumption of materials for type I is 2 kg of materials per fan.

B. The rate of consumption of material for type II is 3 kg of materials per fan.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q49. A product was sold for Rs S at a profit of p% where the cost of manufacturing the product consists of raw materials, labour and overheads. The cost of raw materials, labour and overheads are increased and the company intends to sell the product at a profit. What is the new selling price?

A. Cost for raw materials, labour and overheads are in the ratio of R: L: OH prior to increase in cost.

B. Cost for raw materials, labour and overheads are increased by r%, 1% and oh% respectively.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q50. Three friends, P, Q and R are wearing hats, either black or white. Each person can see the hats of the other two persons. What is thecolour of P’s hat?

A. P says that he can see one black hat and one white hat.

B. Q says that he can see one white hat andone black.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q51. What is the speed of the car?

A. The speed of the car is 10 more than thatof a motorcycle.

B. The motor-cycle takes 2 hours more thanthe car to cover 100 kms.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q52. What is the ratio of the volume of the given right circular cone to the one obtained from it?

A. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1:2.

B. The height and the base of the new cone are one-third those of the original cone.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q53. What is the area bounded by the two lines and the coordinate axes in the first quadrant?

A. The lines intersect at a point which also lies on the lines 3x – 4y = 1 and7x – 8y = 5.

B. The lines are perpendicular, and one of them intersects the y-axis at an intercept of4.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q54. What is the cost price of the chair?

A. The chair and the table are sold, respectively, at a profit of 5% and 20%.

B. If the cost price of the chair is increased by 10% and that of the table is increased by20%, the profit reduces by Rs. 20.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Q55. After what time will the two persons, X and Y meet while moving around the circular track? Both of them start from the same point and at the same time.

A. X moves at a constant speed of 5 m/s,while Y starts at a speed 2 m/s and increases his speed by 0.5 m/s at the end of every second there after.

B. Y can complete one entire lap in exactly 10 seconds.

a. If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

b. If the question can be answered by using either statement alone.

c. If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

d. If the question cannot be answered even by using both the statements together.

 

 

Be a Maths & Reasoning Genius..Beauty Simplified !!!

error:
Skip to toolbar