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CAT Practice Test: Month (March) - CAT MCQ


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30 Questions MCQ Test - CAT Practice Test: Month (March)

CAT Practice Test: Month (March) for CAT 2024 is part of CAT preparation. The CAT Practice Test: Month (March) questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: Month (March) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: Month (March) below.
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CAT Practice Test: Month (March) - Question 1
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In the given figure, straight line AB and CD intersect at O. IF ∠δ =3∠v, then ∠v = ?

Detailed Solution for CAT Practice Test: Month (March) - Question 1

COD is a  straight line 
∴ ∠δ + ∠v =180⁰ ⇒ 3v +v =180 ⇒ 4v = 180 ⇒ v =45⁰.

CAT Practice Test: Month (March) - Question 2
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In a triangle ABC, the incentre is at 0. If ㄥBOC = 100°, find ㄥBAC. 

Detailed Solution for CAT Practice Test: Month (March) - Question 2

In ∠BOC

⇒ x + y = 80°

⇒ 2x + 2y. = 160°

Also, 2x + 2y + 2z = 180°

⇒ 160° + 2z = 180°

⇒ ∠BAC = 2z = 20°

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CAT Practice Test: Month (March) - Question 3
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A rectangular enclosure 40 m x 36 m has a horse tethered to a corner with a rope of 14 m in length. What is the ratio of the respective areas it can graze if it is outside the enclosure and if it is inside the enclosure? 

Detailed Solution for CAT Practice Test: Month (March) - Question 3

  • Imagine a circle on the corner of the rectangle. 
  • 3 quarters of the circle lie outside the rectangle and 1 quarter lies inside. 
  • Hence, Required ratio = 3 : 1
CAT Practice Test: Month (March) - Question 4
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Read the passage below and solve the questions based on it.
The area of a square is equal to the area of a rectangle. Moreover, the perimeter of the square is also equal to the perimeter of the rectangle. 

Q. The length of the rectangle is equal to the: 
Detailed Solution for CAT Practice Test: Month (March) - Question 4

This is possible only when both the length and breadth of the rectangle are equal to the side of the square.

CAT Practice Test: Month (March) - Question 5
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A quadrilateral is inscribed in a circle. If an angle is inscribed in each of the four segments outside the quadrilateral, then what is the sum of these four angles?
Detailed Solution for CAT Practice Test: Month (March) - Question 5

CAT Practice Test: Month (March) - Question 6
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Sagar is 20% more efficient than Pranesh. If Pranesh can complete a piece of work in 30 days, then in how many days can both Sagar and Pranesh complete the work?
Detailed Solution for CAT Practice Test: Month (March) - Question 6

CAT Practice Test: Month (March) - Question 7
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A factory manufactures dyes. It has 12 men and two machines which can be operated by all of its men. It takes 4 hours to manufacture one dye on the machine with the operator. The machines can work continuously without a break. Without the machine each of the men can manufacture a dye in 8 hours. The policy is such that the production is maximized and the men are ready to work in three shifts of 8 hours per day. What will be the average cost incurred per dye if 1 man hour costs Rs 20 and 1 machine hour costs Rs 15?
Detailed Solution for CAT Practice Test: Month (March) - Question 7

To maximize the production, four men will work in each shift. 2 men will work with machines and 2 men work alone.
Total cost incurred in one hour

CAT Practice Test: Month (March) - Question 8
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480 persons working 10 hours per day complete one-fourth of a work in 10 days. How many additional persons are to be employed in order to complete the remaining work in 20 days, working 8 hours per day?
Detailed Solution for CAT Practice Test: Month (March) - Question 8

CAT Practice Test: Month (March) - Question 9
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Anil, Bhuvan and Chandan take 10,20 and 25 days to complete a job. What is the minimum time required to finish the job if not more than 2 of them work together on a single day and no two consecutive days have the same pair of people working?
Detailed Solution for CAT Practice Test: Month (March) - Question 9

Assume total amount of work = 100 units.
A does = 10 units/day, B does = 5 units/day, and C does = 4 units/day
Possible Pairs:
A+B = 15 units/day, A+C = 14 units/day, B+C = 9 units/day
To minimize time, we will use the first two pairs.
So, 15 +14 +15 + 14 + 15 +14 + 15 = 102 units.
So, little less than 7 days are required

Hence, the correct option is 'B'.

CAT Practice Test: Month (March) - Question 10
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Anuj can do a piece of work in a certain number of days. To do the same piece of work, Bhanu takes thrice the number of days as Anuj takes whereas Chandu takes thrice as many days as Bhanu does and Dodo takes thrice as many days as Chandu does. Now, they are paired and two groups are formed. The first pair takes one-third the time taken by the second pair to complete the work, which is the first pair?
Detailed Solution for CAT Practice Test: Month (March) - Question 10

Let Anuj do the work in x days.

 So, Bhanu = 3x days, Chandu = 9x days and Dodo = 27x days

Now, using options,

Anuj + Chandu = 1/x + l/9x = 10/9x,

So, they take 9x/10 days

Bhanu + Dodo = l/3x + 1/27x = 10/27x, So, they take 27x/10 days

Now, 1/3 of 27x/ 10 = 9x /10.

 So, Anuj and Chandu is first pair.

CAT Practice Test: Month (March) - Question 11
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A jeep travels a distance of 100 km at a uniform speed. If the speed of the jeep is 5 kmph more, then it takes 1 hour less to cover the same distance. The original speed of the jeep is:
Detailed Solution for CAT Practice Test: Month (March) - Question 11

The original speed of the jeep is 20 kmph.

Let the original speed of the jeep be x kmph.

Time taken to cover 100 km at original speed = 100/x hours.

Time taken to cover 100 km at increased speed = 100/(x+5) hours.

Given that the time taken to cover 100 km at increased speed is 1 hour less than the time taken to cover 100 km at original speed.

Therefore, 100/x - 100/(x+5) = 1

Solving for x, we get x = 20.

Hence, the original speed of the jeep is 20 kmph.

CAT Practice Test: Month (March) - Question 12
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Two athletes cover the same distance at the rate of 10 and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.
Detailed Solution for CAT Practice Test: Month (March) - Question 12

The distance travelled is 7.5 km.

Let the time taken by the athlete travelling at 10 kmph be t hours.

The time taken by the athlete travelling at 15 kmph is t+15/60 hours.

The distance travelled by both athletes is the same.

Therefore, 10t = 15(t+15/60)

Solving for t, we get t = 3/4 hours.

The distance travelled by both athletes is 10t = 10 * 3/4 = 7.5 km.

CAT Practice Test: Month (March) - Question 13
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If Sita walks at 5 kmph, she misses her train by 10 minutes. If she walks at 7 kmph, she reaches the station 10 minutes early. How much distance does she walk to the station?
Detailed Solution for CAT Practice Test: Month (March) - Question 13

The distance to the station can be calculated as follows:

Let's denote the distance to the station as "d" (in km), and the time difference between the two cases as "t" (in minutes).

In the first case, Sita walks at 5 km/h and misses the train by 10 minutes. So the time it would take her to get to the train on time is: d/5 (in hours) + 10/60 (in hours) = d/5 + 1/6 (in hours).

In the second case, Sita walks at 7 km/h and arrives 10 minutes early. So the time it takes her to get to the train is: d/7 - 10/60 = d/7 - 1/6 (in hours).

Since these two times should be the same, we can equate them:

d/5 + 1/6 = d/7 - 1/6

Solving this equation for "d" gives:

d = 35/6 km = 5.8 km

So the correct answer is 5.8 km.

CAT Practice Test: Month (March) - Question 14
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A friend is spotted by Lalloo at a distance of 200 m. When Lalloo starts to approach him, the friend also starts moving in the same direction as Lalloo. If the speed of his friend is 15 kmph, and that of Lalloo is 20 kmph, then how far will the friend have to walk before Lalloo meets him?
Detailed Solution for CAT Practice Test: Month (March) - Question 14

Lalloo is unfortunate that the friend is moving away from him.

(Because the friend moves in same direction as Lalloo).

relative speed= 20- 15= 5,kmph. distance= 200 m.

Thus, Lalloo will meet his friend when he gains 200 m over him.

=> time required = distance / speed = 0.2/5 = 1/25 hrs.

=> Distance travelled by the friend in 1/25 hrs. (when Lalloo catches up him)

=> Time x Speed = 1/25 x 15 = 3/5 km = 600 m

CAT Practice Test: Month (March) - Question 15
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A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the speed of the train is three times that of the horse-transit and 1(1/2) times that of the steamer. Find the speed of the train.
Detailed Solution for CAT Practice Test: Month (March) - Question 15

To find the speed of the train, we first need to find the speed of the steamer and the speed of the horse transit. The total distance traveled is 120 km + 450 km + 60 km = 630 km, and the total time taken for the journey is 13.5 hours. Therefore, the average speed of the journey is 630 km / 13.5 hours = 46.67 km/hr.

Since the speed of the train is three times that of the horse-transit and 1.5 times that of the steamer, we can write the following equations:

t = 3h t = 1.5s

where t is the speed of the train, h is the speed of the horse transit, and s is the speed of the steamer. Solving these equations, we find that the speed of the horse transit is 23.01 km/hr and the speed of the train is 69.03 km/hr.

Therefore, the speed of the train is 69.03 km/hr. The correct answer is B

CAT Practice Test: Month (March) - Question 16
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A right circular cone of radius K cm and height 24 cm rests on the base of a right circular cylinder of radius K cm (their bases lie in the same plane, as shown in the figure). The cylinder is filled with water to a height of 24 cm. If the cone is then removed, to which height will the water fall?
Detailed Solution for CAT Practice Test: Month (March) - Question 16

Height of water in the cylinder before the cone is taken out = 24 cm
Volume of water in the cylinder before the cone is taken out = Volume of cone + Volume of water
Let H be the height of the water level after the cone is taken out.




H = 16 cm

CAT Practice Test: Month (March) - Question 17
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The curved surface areas of two spheres are in the ratio of 1 : 4. Find the ratio of their volumes.
Detailed Solution for CAT Practice Test: Month (March) - Question 17

Let the two spheres be A and B.

CAT Practice Test: Month (March) - Question 18
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The ratio of the volume of a sphere to its surface area is  
Detailed Solution for CAT Practice Test: Month (March) - Question 18

Volume of a sphere

Surface area = 4πr2 

Ratio of the volume to the surface area = r : 3

CAT Practice Test: Month (March) - Question 19
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A right-circular cone is carved out of a cube having the same height and radius, equal to half the side of the cube. What is the ratio of the volume of the carved cone to that of the cube left after carving?
Detailed Solution for CAT Practice Test: Month (March) - Question 19

Given height and diameter:

CAT Practice Test: Month (March) - Question 20
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The sector of a circle with radius 10 cm and angle 120° is rolled up such that the two bounding radii are joined together to form a cone. Find the volume of the cone.
Detailed Solution for CAT Practice Test: Month (March) - Question 20


Length of arc AXB = Circumference of the base of the cone

= 20.95 cm
Let the radius of the base be r.
So, 2πr = 20.95

44r = 146.65 
r = 146.65/44
r = 3.33 cm
Now, to find out height we can use Pythagorean theorem.
Let the height of the cone be h.
So, h2 = R2 - r2
h2 = 100 - 11.08

h = 9.42 cm
Now, volume of the cone 


= 109.3 cm3

CAT Practice Test: Month (March) - Question 21
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Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer:
- (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.

Question: Who among P, Q, R, S and T is the lightest?
Statements:
I.R is heavier than Q and T but lighter than S.
II.S is not the heaviest.
Detailed Solution for CAT Practice Test: Month (March) - Question 21

From I, we have: R>Q, R>T, S>R i.e. S>R>Q>T or S>R>T>Q.

From II, S is not the heaviest. So, P is the heaviest. Thus, we have: P > S > R > Q > T or P > S > R > T > Q. Hence, either T or Q is the lightest.

CAT Practice Test: Month (March) - Question 22
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Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer:
- (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.

Question: How is T related to K?
Statements:
I.K has two sons; one of the sons is A.
II.The mother of T has only two sons - Aand B.
Detailed Solution for CAT Practice Test: Month (March) - Question 22

From II, we know that T's mother has only two sons, A and B. This implies that T is the sister of both A and B. But, from I, A is also K's son. So, T is the daughter of K.

CAT Practice Test: Month (March) - Question 23
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Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer:
- (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.

Question: What is the shortest distance between Devipur and Durgapur ?
Statements:
I.Durgapur is 20 kms away from Rampur.
II.Devipur is 15 kms away from Rampur.
Detailed Solution for CAT Practice Test: Month (March) - Question 23

Clearly, the distance of each village from Rampur is given in I and II. But nothing about their relative positions is mentioned. So, the distance between the two villages cannot be calculated.

CAT Practice Test: Month (March) - Question 24
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Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer:
- (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.

Question: Manoj, Prabhakar, Akash and Kamal are four friends. Who among them is the heaviest ?
Statements:
I.Prabhakar is heavier than Manoj and Kamal but lighter than Akash.
II.Manoj is lighter than Prabhakar and Akash but heavier than Kamal.
Detailed Solution for CAT Practice Test: Month (March) - Question 24

From I, we have: P > M, P > K, A > P.

Thus, A > P > M > K or A > P > K > M. So, Akash is the heaviest.

From II, we have: P > M, A > M, M > K.

Thus, A > P > M > K or P > A > M > K. So, either Akash or Prabhakar is the heaviest.

CAT Practice Test: Month (March) - Question 25
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Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and

Give answer:
- (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.

Question: How is A related to D ?
Statements:
I.B is the brother of A.
II.B is D's son.
Detailed Solution for CAT Practice Test: Month (March) - Question 25

From I and II, we conclude that A is either son or daughter of D.

CAT Practice Test: Month (March) - Question 26
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Directions: Study the following graph and answer the question that follows.

POWER PRODUCTION OF A COMPANY (IN MILLION WATTS)


Q. What is the difference between the peak hydel power production and the least Hydel Power Production ?
Detailed Solution for CAT Practice Test: Month (March) - Question 26

Difference between the peak hydel power production and the least hydel power production = 180 - 100 = 80 million watts
So, option (4) is correct.

CAT Practice Test: Month (March) - Question 27
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Directions: Study the following graph and answer the question that follows.

POWER PRODUCTION OF A COMPANY (IN MILLION WATTS)

Q. In which year is the total power production (thermal + hydel) the greatest?
Detailed Solution for CAT Practice Test: Month (March) - Question 27

Total power production (thermal and hydel) in 1990 = 140 + 140 = 280 million watts
Total power production (thermal and hydel) in 1991 = 140 + 180 = 320 million watts
Total power production (thermal and hydel) in 1992 = 100 + 120 = 220 million watts
Total power production (thermal and hydel) in 1993 = 150 + 130 = 280 million watts
Total power production (thermal and hydel) in 1994 = 155 + 145 = 300 million watts
Total power production (thermal and hydel) in 1995 = 153 + 141 = 294 million watts
Total power production (thermal and hydel) in 1996 = 145 + 145 = 290 million watts
The total power production is the greatest in 1991, i.e. 320 million watt.

CAT Practice Test: Month (March) - Question 28
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Directions: Study the following graph and answer the question that follows.

POWER PRODUCTION OF A COMPANY (IN MILLION WATTS)

Q. What is the average thermal power production for the period 1990-1996?
Detailed Solution for CAT Practice Test: Month (March) - Question 28

Required average = = 141.85 million watts

Hence, option (4) is correct.

CAT Practice Test: Month (March) - Question 29
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Directions: Study the following graph carefully and answer the question given below.

Q. If the population of a city is 35,000 and the average income of a person in that city is Rs. 25,000 per annum, then what is the total amount of tax paid by all the persons of that city?
Detailed Solution for CAT Practice Test: Month (March) - Question 29

Tax paid by one person of that city = 8/100 x 25,000 = Rs. 2000

Total tax paid by all the persons of that city = 2000 × 35,000 = Rs. 70,000,000

CAT Practice Test: Month (March) - Question 30
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Directions: Study the following graph carefully and answer the question given below.

Q. What is the total amount of tax on an income of Rs. 9000 and an income of Rs. 2000?
Detailed Solution for CAT Practice Test: Month (March) - Question 30

Tax on income of Rs. 2000 = 1% of 2000 = Rs. 20
Tax on income of Rs. 9000 = 2% of 9000 = Rs. 180
Total tax on an income of Rs. 2000 and an income of Rs. 9000 = 20 + 180 = Rs. 200

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