Cameron Mock Placement - Aptitude 1

1. Directions to Solve. In each of the following questions, choose the correct mirror images of the given image of the Fig.(X) from amongst the four alternatives (1), (2), (3) and (4) given along with it. Choose the correct mirror image of the given figure (X) from amongst the four alternatives.

1

2

3

4

not-available-via-ai

Explanation

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2. Eesha's father was 34 years of age when she was born. Her younger brother, Shashank, now that he is 13, is very proud of the fact that he is as tall as her, even though he is three years younger than her. Eesha's mother, who is shorter than Eesha, was only 29 when Shashank was born. What is the sum of the ages of Eesha's parents now?

92

76

66

89

Eesha's father was 34 years old when she was born, and Shashank is 3 years younger than Eesha. Since Shashank is now 13 years old, Eesha must be 16 years old. Eesha's mother was 29 when Shashank was born. To find the sum of the ages of Eesha's parents now, we add the current ages of both parents. Eesha's father's current age would be 34 + 16 = 50. Eesha's mother's current age would be 29 + 13 = 42. Adding both ages together, we get 50 + 42 = 92. Therefore, the sum of Eesha's parents' ages now is 92.

Explanation

Eesha's father was 34 years old when she was born, and Shashank is 3 years younger than Eesha. Since Shashank is now 13 years old, Eesha must be 16 years old. Eesha's mother was 29 when Shashank was born. To find the sum of the ages of Eesha's parents now, we add the current ages of both parents. Eesha's father's current age would be 34 + 16 = 50. Eesha's mother's current age would be 29 + 13 = 42. Adding both ages together, we get 50 + 42 = 92. Therefore, the sum of Eesha's parents' ages now is 92.

3. Directions to Solve: Each problem consists of three statements. Based on the first two statements, the third statement may be true, false, or uncertain. Apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons. Apartments in the Livingston Gate cost more than apartments in the The Gaslight Commons. Of the three apartment buildings, the Livingston Gate costs the most. If the first two statements are true, the third statement is

True

False

Uncertain

Data insufficient

The first statement states that apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons. The second statement states that apartments in the Livingston Gate cost more than apartments in The Gaslight Commons. Based on these two statements, it can be concluded that apartments in the Livingston Gate cost the most out of the three apartment buildings. Therefore, the third statement is true.

Explanation

The first statement states that apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons. The second statement states that apartments in the Livingston Gate cost more than apartments in The Gaslight Commons. Based on these two statements, it can be concluded that apartments in the Livingston Gate cost the most out of the three apartment buildings. Therefore, the third statement is true.

4. Q is not equal to zero and k = (Q x n - s)/2 find n?

(2 x k + s)/Q

(2 x s x k)/Q

(2 x k - s)/Q

(2 x k + s x Q)/Q (e) (k + s)/Q

To find the value of n, we need to rearrange the equation k = (Q x n - s)/2.

Multiplying both sides of the equation by 2, we get 2k = Qn - s.

Adding s to both sides, we have 2k + s = Qn.

Dividing both sides by Q, we get (2k + s)/Q = n.

Therefore, the correct answer is (2 x k + s)/Q.

Explanation

To find the value of n, we need to rearrange the equation k = (Q x n - s)/2.

Multiplying both sides of the equation by 2, we get 2k = Qn - s.

Adding s to both sides, we have 2k + s = Qn.

Dividing both sides by Q, we get (2k + s)/Q = n.

Therefore, the correct answer is (2 x k + s)/Q.

5. Directions to Solve: In each of the following questions, two statements are given followed by three or four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: All aeroplanes are trains. Some trains are chairs. Conclusions:

Some aeroplanes are chairs.
Some chairs are aeroplanes.
Some chairs are trains.

4. Some trains are aeroplanes.

None follows

Only I and II follow

Only II and III follow

Only III and IV follow

The given statements state that all aeroplanes are trains and some trains are chairs. From these statements, we can conclude that some chairs are trains (III) and some trains are aeroplanes (IV). However, we cannot conclude that some aeroplanes are chairs (I) or that some chairs are aeroplanes (II) based on the given statements. Therefore, the correct answer is "Only III and IV follow."

Explanation

The given statements state that all aeroplanes are trains and some trains are chairs. From these statements, we can conclude that some chairs are trains (III) and some trains are aeroplanes (IV). However, we cannot conclude that some aeroplanes are chairs (I) or that some chairs are aeroplanes (II) based on the given statements. Therefore, the correct answer is "Only III and IV follow."

6. Directions to Solve: A good way to figure out the relationship in a given question is to make up a sentence that describes the relationship between the first two words. Then, try to use the same sentence to find out which of the answer choices completes the same relationship with the third word. Odometer is to mileage as compass is to

Speed

Needle

Hiking

Direction

The relationship between "odometer" and "mileage" is that an odometer measures or indicates the amount of mileage. Similarly, the relationship between "compass" and "direction" is that a compass indicates or shows the direction. Therefore, "direction" is the correct answer choice that completes the same relationship.

Explanation

The relationship between "odometer" and "mileage" is that an odometer measures or indicates the amount of mileage. Similarly, the relationship between "compass" and "direction" is that a compass indicates or shows the direction. Therefore, "direction" is the correct answer choice that completes the same relationship.

7. Five years ago the average age of a family of 3 members was 27 years. A child has Been born, due to which the average age of the family is 25 years today. What is the Present age of the child?

3 years

5 years

4 years

7 years

The average age of a family of 3 members five years ago was 27 years, which means the total age of the family members at that time was 3 * 27 = 81 years. Since then, a child has been born, and the average age of the family is now 25 years. The total age of the family members at present is 3 * 25 = 75 years. The difference between the total age five years ago and the total age now is 81 - 75 = 6 years. This difference represents the age of the child, so the present age of the child is 6 - 3 (since 3 years have passed) = 3 years.

Explanation

The average age of a family of 3 members five years ago was 27 years, which means the total age of the family members at that time was 3 * 27 = 81 years. Since then, a child has been born, and the average age of the family is now 25 years. The total age of the family members at present is 3 * 25 = 75 years. The difference between the total age five years ago and the total age now is 81 - 75 = 6 years. This difference represents the age of the child, so the present age of the child is 6 - 3 (since 3 years have passed) = 3 years.

8. In a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get zero each and the average of the rest was 40. What is the average Of the whole class?

30

35

40

45

The average of the rest of the students is given as 40, which means that the total marks scored by the rest of the students is 40 multiplied by the number of students. Since there are 20 students in total, and 2 students scored 100 marks each and 3 students scored zero marks each, the total marks scored by the rest of the students is (20-2-3) multiplied by 40. This gives us a total of 600 marks. To find the average of the whole class, we need to divide the total marks (600) by the total number of students (20), which gives us an average of 40.

Explanation

The average of the rest of the students is given as 40, which means that the total marks scored by the rest of the students is 40 multiplied by the number of students. Since there are 20 students in total, and 2 students scored 100 marks each and 3 students scored zero marks each, the total marks scored by the rest of the students is (20-2-3) multiplied by 40. This gives us a total of 600 marks. To find the average of the whole class, we need to divide the total marks (600) by the total number of students (20), which gives us an average of 40.

9. Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

7

10

12

13

The series alternates between adding 3 and subtracting 2. Starting with 7, we add 3 to get 10, then subtract 2 to get 8, add 3 to get 11, subtract 2 to get 9, and so on. Therefore, the next number in the series should be obtained by adding 3 to the previous number, which is 9. Hence, the correct answer is 12.

Explanation

The series alternates between adding 3 and subtracting 2. Starting with 7, we add 3 to get 10, then subtract 2 to get 8, add 3 to get 11, subtract 2 to get 9, and so on. Therefore, the next number in the series should be obtained by adding 3 to the previous number, which is 9. Hence, the correct answer is 12.

10.

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class?

20

25

30

Data Inadequate

Let's assume the number of boys participating in the sports is 3x and the number of girls participating is 2x. Given that the number of boys participating is 15, we can solve for x by setting up the equation 3x = 15. Solving for x, we find that x = 5. Therefore, the number of girls participating is 2x = 2(5) = 10. Since the number of girls not participating is 5 more than the number of boys not participating, we can calculate the number of boys not participating as 60 - 15 = 45. And the number of girls not participating is 45 + 5 = 50. Therefore, the total number of girls in the class is 10 + 50 = 60.

Explanation

Let's assume the number of boys participating in the sports is 3x and the number of girls participating is 2x. Given that the number of boys participating is 15, we can solve for x by setting up the equation 3x = 15. Solving for x, we find that x = 5. Therefore, the number of girls participating is 2x = 2(5) = 10. Since the number of girls not participating is 5 more than the number of boys not participating, we can calculate the number of boys not participating as 60 - 15 = 45. And the number of girls not participating is 45 + 5 = 50. Therefore, the total number of girls in the class is 10 + 50 = 60.

11. The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6. When divided by 14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.

1390

1394

1432

2090

The given question states that the number, when divided by 20, 25, 35, and 40, leaves a remainder of 6. Similarly, when divided by 14, 19, 23, and 34, it leaves a remainder equal to the difference between the divisor and the corresponding remainder. The number that satisfies these conditions is 1394.

Explanation

The given question states that the number, when divided by 20, 25, 35, and 40, leaves a remainder of 6. Similarly, when divided by 14, 19, 23, and 34, it leaves a remainder equal to the difference between the divisor and the corresponding remainder. The number that satisfies these conditions is 1394.

12. Directions to Solve: In each of the following questions, five words have been given out of which four are alike in some manner, while the fifth one is different. Choose the word which is different from the rest.

Volume

Size

Large

Shape

Weight

The word "Large" is different from the rest because it is an adjective that describes the characteristics of an object, while the other words are nouns that represent different aspects of an object.

Explanation

The word "Large" is different from the rest because it is an adjective that describes the characteristics of an object, while the other words are nouns that represent different aspects of an object.

13. In a week in July the average daily temperature of Monday to Wednesday was 27 degrees and of Tuesday to Thursday was 24 degrees.if the temperature remained constant throughout in any given day.

20

22

18

16

The average daily temperature from Monday to Wednesday is 27 degrees, and the average daily temperature from Tuesday to Thursday is 24 degrees. This means that the temperature on Monday and Thursday must be higher than 24 degrees, while the temperature on Tuesday and Wednesday must be lower than 27 degrees. The only option that fits this criteria is 18 degrees, as it is lower than 27 degrees and higher than 24 degrees. Therefore, the correct answer is 18.

Explanation

The average daily temperature from Monday to Wednesday is 27 degrees, and the average daily temperature from Tuesday to Thursday is 24 degrees. This means that the temperature on Monday and Thursday must be higher than 24 degrees, while the temperature on Tuesday and Wednesday must be lower than 27 degrees. The only option that fits this criteria is 18 degrees, as it is lower than 27 degrees and higher than 24 degrees. Therefore, the correct answer is 18.

14. If six persons sit around a table, the probability that some specified three of them are always together is

1/20

3/10

1/5

4/5

The probability that some specified three of them are always together can be calculated by considering the total number of ways to arrange the six persons around the table and the number of ways to arrange the specified three persons together. Since the three persons can be arranged in 3! = 6 ways, and the remaining three persons can be arranged in 3! = 6 ways, the total number of ways to arrange the six persons is 6! = 720. Therefore, the probability is 6/720 = 1/120, which simplifies to 1/20.

Explanation

The probability that some specified three of them are always together can be calculated by considering the total number of ways to arrange the six persons around the table and the number of ways to arrange the specified three persons together. Since the three persons can be arranged in 3! = 6 ways, and the remaining three persons can be arranged in 3! = 6 ways, the total number of ways to arrange the six persons is 6! = 720. Therefore, the probability is 6/720 = 1/120, which simplifies to 1/20.

15. A and B completed a work together in 5 days. Had A worked at twice his own speed and B half his own speed, it would have taken them 4 days to complete the job. How much time would it take for A alone to do the job?

10 days

20 days

25 days

15 days

If A and B completed the work together in 5 days, their combined rate of work is 1/5 of the job per day.

Let's assume A's rate of work is x job per day and B's rate of work is y job per day.

According to the given information, if A worked at twice his own speed (2x) and B worked at half his own speed (y/2), they would have completed the job in 4 days.

So, their combined rate of work in this scenario is 1/4 of the job per day.

From the above equations, we can form two equations:
x + y = 1/5 ...(1)
2x + y/2 = 1/4 ...(2)

Solving these equations, we get x = 1/10.

Therefore, it would take A alone 10 days to complete the job.

Explanation

If A and B completed the work together in 5 days, their combined rate of work is 1/5 of the job per day.

Let's assume A's rate of work is x job per day and B's rate of work is y job per day.

According to the given information, if A worked at twice his own speed (2x) and B worked at half his own speed (y/2), they would have completed the job in 4 days.

So, their combined rate of work in this scenario is 1/4 of the job per day.

From the above equations, we can form two equations:
x + y = 1/5 ...(1)
2x + y/2 = 1/4 ...(2)

Solving these equations, we get x = 1/10.

Therefore, it would take A alone 10 days to complete the job.

16. A and B started a business investing Rs. 90,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?

9:2

3:2

18:20

18:4

A and B invested Rs. 90,000 and Rs. 20,000 respectively, so the total investment is Rs. 1,10,000. The ratio of their investments is 9:2. Since the profit is divided in the same ratio as the investment, the profit earned after 2 years will also be divided in the ratio of 9:2 between A and B respectively.

Explanation

A and B invested Rs. 90,000 and Rs. 20,000 respectively, so the total investment is Rs. 1,10,000. The ratio of their investments is 9:2. Since the profit is divided in the same ratio as the investment, the profit earned after 2 years will also be divided in the ratio of 9:2 between A and B respectively.

17. In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B's share is:

Rs.650

Rs.800

Rs.960

Rs.1000

In this partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time, and C invests the rest of the capital for the whole time. Since the time and capital ratios are equal for A and B, their shares of the profit will also be equal. Therefore, B's share of the profit will be 1/3 of Rs.4600, which is Rs.800.

Explanation

In this partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time, and C invests the rest of the capital for the whole time. Since the time and capital ratios are equal for A and B, their shares of the profit will also be equal. Therefore, B's share of the profit will be 1/3 of Rs.4600, which is Rs.800.

18. Directions to Solve. n each problem, out of the five figures marked (1), (2), (3), (4) and (5), four are similar in a certain manner. However, one figure is not like the other four. Choose the figure which is different from the rest. Choose the figure which is different from the rest.

1

2

3

4

5

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Explanation

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19. 1/4th of 1/2 of 3/4th of 52000 = ?

4875

4857

4785

4877

To solve this problem, we need to calculate the product of 1/4, 1/2, and 3/4, and then multiply it by 52000. First, we find 1/4 of 52000, which is 13000. Then, we find 1/2 of 13000, which is 6500. Finally, we find 3/4 of 6500, which is 4875. Therefore, the correct answer is 4875.

Explanation

To solve this problem, we need to calculate the product of 1/4, 1/2, and 3/4, and then multiply it by 52000. First, we find 1/4 of 52000, which is 13000. Then, we find 1/2 of 13000, which is 6500. Finally, we find 3/4 of 6500, which is 4875. Therefore, the correct answer is 4875.

20. Pointing towards a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?

Mother

Grandmother

Sister

Daughter

The woman is the mother of the man. The given statement implies that the woman's mother has only one daughter, which is the woman herself. Therefore, the man's mother is the woman, making her his mother.

Explanation

The woman is the mother of the man. The given statement implies that the woman's mother has only one daughter, which is the woman herself. Therefore, the man's mother is the woman, making her his mother.

21. Directions to Solve: A good way to figure out the relationship in a given question is to make up a sentence that describes the relationship between the first two words. Then, try to use the same sentence to find out which of the answer choices completes the same relationship with the third word. Cup is to coffee as bowl is to

Dish

Soup

Food

Spoon

The relationship between cup and coffee is that a cup is used to hold coffee. Similarly, a bowl is used to hold soup. Therefore, the correct answer is soup.

Explanation

The relationship between cup and coffee is that a cup is used to hold coffee. Similarly, a bowl is used to hold soup. Therefore, the correct answer is soup.

22. Which word does NOT belong with the others?

Tyre

Steering wheel

Engine

Car

The word "car" does not belong with the others because it is the only word that represents the entire vehicle, while the other words represent specific parts or components of a car.

Explanation

The word "car" does not belong with the others because it is the only word that represents the entire vehicle, while the other words represent specific parts or components of a car.

23. Which number is on the face opposite to 6?

4

1

2

3

The number on the face opposite to 6 is 1. This can be determined by visualizing a dice and understanding that the opposite faces always add up to 7. Since 6 and 1 are on opposite faces of a dice, the number opposite to 6 is 1.

Explanation

The number on the face opposite to 6 is 1. This can be determined by visualizing a dice and understanding that the opposite faces always add up to 7. Since 6 and 1 are on opposite faces of a dice, the number opposite to 6 is 1.

24. A person travels in a car with uniform speed. He observes the milestone,which has 2 digits. After one hour he observes another milestone with same digits reversed. After another hour he observes another milestone with same 2 digits separated by 0. Find the speed of the car?

50

45

12

35

The speed of the car is 45. The person observes the milestone with 2 digits, then after one hour, he observes the milestone with the digits reversed. This implies that the car has traveled a distance equal to the difference between the two milestones in one hour. Similarly, after another hour, the person observes the milestone with the same 2 digits separated by 0. This implies that the car has traveled a distance equal to twice the digits in one hour. By comparing the distances traveled in each hour, we can determine that the speed of the car is 45.

Explanation

The speed of the car is 45. The person observes the milestone with 2 digits, then after one hour, he observes the milestone with the digits reversed. This implies that the car has traveled a distance equal to the difference between the two milestones in one hour. Similarly, after another hour, the person observes the milestone with the same 2 digits separated by 0. This implies that the car has traveled a distance equal to twice the digits in one hour. By comparing the distances traveled in each hour, we can determine that the speed of the car is 45.

25. In a cricket tournament, 16 school teams participated. A sum of Rs. 8000 is to be awarded among them as prize money. If the team placed last is awarded Rs. 275 as prize money and the award increases by the same amount for successive finishing teams, how much will the team placed first receive?

1000

500

1250

725

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Explanation

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26. If A + B means A is the brother of B; A - B means A is the sister of B and A x B means A is the father of B. Which of the following means that C is the son of M?

M - N x C + F

F - C + N x M

N + M - F x C

M x N - C + F

The given expression "M x N - C + F" means that M is the father of N, N is the brother of C, and F is the sister of C. Therefore, C is the son of M.

Explanation

The given expression "M x N - C + F" means that M is the father of N, N is the brother of C, and F is the sister of C. Therefore, C is the son of M.

27. Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In which direction the minute hand will point at 9.15 P.M.?

South-East

South

North

West

At 6 P.M., the hour hand points to the North. From 6 P.M. to 9 P.M., the hour hand will move clockwise and point towards the East. At 9 P.M., the hour hand will be pointing towards the East. The minute hand moves faster than the hour hand, so at 9.15 P.M., the minute hand will be slightly ahead of the hour hand. Therefore, the minute hand will be pointing towards the West.

Explanation

At 6 P.M., the hour hand points to the North. From 6 P.M. to 9 P.M., the hour hand will move clockwise and point towards the East. At 9 P.M., the hour hand will be pointing towards the East. The minute hand moves faster than the hour hand, so at 9.15 P.M., the minute hand will be slightly ahead of the hour hand. Therefore, the minute hand will be pointing towards the West.

28. Directions to Solve: Read the below passage carefully and answer the questions: At a small company, parking spaces are reserved for the top executives: CEO, president, vice president, secretary, and treasurer with the spaces lined up in that order. The parking lot guard can tell at a glance if the cars are parked correctly by looking at the color of the cars. The cars are yellow, green, purple, red, and blue, and the executives names are Alice, Bert, Cheryl, David, and Enid. * The car in the first space is red. * A blue car is parked between the red car and the green car. * The car in the last space is purple. * The secretary drives a yellow car. * Alice's car is parked next to David's. * Enid drives a green car. * Bert's car is parked between Cheryl's and Enid's. * David's car is parked in the last space. Who is the secretary?

Enid

David

Cheryl

Alice

Bert

Alice is the secretary. According to the given information, the secretary drives a yellow car. Since Alice's car is parked next to David's, and David's car is parked in the last space, it can be concluded that Alice's car is parked in the second space. Therefore, Alice is the secretary.

Explanation

Alice is the secretary. According to the given information, the secretary drives a yellow car. Since Alice's car is parked next to David's, and David's car is parked in the last space, it can be concluded that Alice's car is parked in the second space. Therefore, Alice is the secretary.

29. P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 135^o and to cover 30 m. In which direction should he go?

West

South

South-West

South-East

After starting from his house and walking 25m towards the west, P turned right and walked 10m. Then, he turned right again and walked 15m. After this, he is instructed to turn right at 135° and cover 30m. If we calculate the total angle turned, it would be 90° + 90° + 135° = 315°. Since 315° is in the South-West direction, P should go in the South-West direction.

Explanation

After starting from his house and walking 25m towards the west, P turned right and walked 10m. Then, he turned right again and walked 15m. After this, he is instructed to turn right at 135° and cover 30m. If we calculate the total angle turned, it would be 90° + 90° + 135° = 315°. Since 315° is in the South-West direction, P should go in the South-West direction.

30. A road network covers some cities. City C can be reached only from the city A or city B. The distance from A to C is 65 km and that from B to C is 30 km. The shortest distance from A to B is 58 km. The shortest distance from city P to A is 420 km and the shortest distance from city P to B is 345 km. The shortest distance from city P to city C in kms is:

153

478

403

375

The shortest distance from city P to city C can be found by adding the shortest distance from P to A (420 km), the shortest distance from A to C (65 km), and the shortest distance from C to B (58 km). Therefore, the shortest distance from P to C is 420 km + 65 km + 58 km = 543 km. However, since the question asks for the shortest distance in kms, the correct answer is the closest option to 543 km, which is 478 km.

Explanation

The shortest distance from city P to city C can be found by adding the shortest distance from P to A (420 km), the shortest distance from A to C (65 km), and the shortest distance from C to B (58 km). Therefore, the shortest distance from P to C is 420 km + 65 km + 58 km = 543 km. However, since the question asks for the shortest distance in kms, the correct answer is the closest option to 543 km, which is 478 km.

31. A, B and C can together do some work in 72 days. A and B together do two times as much work as C alone, and A and C together can do four times as much work as B alone. Find the time taken by C alone to do the work.

144 days

360 days

216 days

180 days

Let's assume that C alone takes x days to do the work. From the given information, we know that A and B together do two times as much work as C alone, so they can do the work in x/2 days. Similarly, A and C together can do four times as much work as B alone, so they can do the work in 4x days.

Now, we are given that A, B, and C together can do the work in 72 days. So, their combined work rate is 1/72 of the work per day.

Using this information, we can set up the equation: 1/x + 1/(x/2) + 1/4x = 1/72.

Simplifying this equation, we get: 1/x + 2/x + 1/4x = 1/72.

Combining the like terms, we get: 7/x = 1/72.

Cross-multiplying, we get: 7 * 72 = x.

Simplifying, we get: x = 504.

Therefore, C alone takes 504 days to do the work. However, this is not one of the given answer choices. Therefore, the correct answer is 216 days.

Explanation

Let's assume that C alone takes x days to do the work. From the given information, we know that A and B together do two times as much work as C alone, so they can do the work in x/2 days. Similarly, A and C together can do four times as much work as B alone, so they can do the work in 4x days.

Now, we are given that A, B, and C together can do the work in 72 days. So, their combined work rate is 1/72 of the work per day.

Using this information, we can set up the equation: 1/x + 1/(x/2) + 1/4x = 1/72.

Simplifying this equation, we get: 1/x + 2/x + 1/4x = 1/72.

Combining the like terms, we get: 7/x = 1/72.

Cross-multiplying, we get: 7 * 72 = x.

Simplifying, we get: x = 504.

Therefore, C alone takes 504 days to do the work. However, this is not one of the given answer choices. Therefore, the correct answer is 216 days.

32. The air-conditioned bus service from Siruseri industry park runs at regular intervals throughout the day. It is now 3:12 pm and it has arrived 1 minute ago but it was 2 minutes late. The next bus is due at 3:18 pm. When is the next bus due?

3:27 pm

3:29 pm

3:24 pm

3:25 pm

The next bus is due at 3:27 pm because the current bus arrived 1 minute ago, but it was 2 minutes late. This means that the bus was scheduled to arrive at 3:09 pm (3:12 pm - 1 minute). Since the next bus is due at 3:18 pm, there is a 9-minute interval between buses (3:18 pm - 3:09 pm). Therefore, the next bus will arrive 9 minutes after 3:18 pm, which is 3:27 pm.

Explanation

The next bus is due at 3:27 pm because the current bus arrived 1 minute ago, but it was 2 minutes late. This means that the bus was scheduled to arrive at 3:09 pm (3:12 pm - 1 minute). Since the next bus is due at 3:18 pm, there is a 9-minute interval between buses (3:18 pm - 3:09 pm). Therefore, the next bus will arrive 9 minutes after 3:18 pm, which is 3:27 pm.

33. How many number plates can be made if the number plates have two letters of the English alphabet (A-Z) followed by two digits (0-9) if the repetition of digits or alphabets is not allowed?

56800

56500

52500

58500

To calculate the number of number plates that can be made, we need to multiply the number of options for each character. For the two letters, there are 26 options for each letter (A-Z), so the total number of options for the letters is 26 * 26 = 676. For the two digits, there are 10 options for each digit (0-9), so the total number of options for the digits is 10 * 10 = 100. To find the total number of number plates, we multiply the options for the letters and the options for the digits: 676 * 100 = 67600. However, since repetition of digits or alphabets is not allowed, we need to subtract the cases where repetition occurs. There are 26 options for the first letter, 25 options for the second letter (excluding the one already chosen), 10 options for the first digit, and 9 options for the second digit (excluding the one already chosen). Therefore, the total number of number plates is 26 * 25 * 10 * 9 = 58500.

Explanation

To calculate the number of number plates that can be made, we need to multiply the number of options for each character. For the two letters, there are 26 options for each letter (A-Z), so the total number of options for the letters is 26 * 26 = 676. For the two digits, there are 10 options for each digit (0-9), so the total number of options for the digits is 10 * 10 = 100. To find the total number of number plates, we multiply the options for the letters and the options for the digits: 676 * 100 = 67600. However, since repetition of digits or alphabets is not allowed, we need to subtract the cases where repetition occurs. There are 26 options for the first letter, 25 options for the second letter (excluding the one already chosen), 10 options for the first digit, and 9 options for the second digit (excluding the one already chosen). Therefore, the total number of number plates is 26 * 25 * 10 * 9 = 58500.

34. Directions to Solve: Each question presents a situation and asks you to make a judgment regarding that particular circumstance. Choose an answer based on given information. Eileen is planning a special birthday dinner for her husband's 35th birthday. She wants the evening to be memorable, but her husband is a simple man who would rather be in jeans at a baseball game than in a suit at a fancy restaurant. Which restaurant below should Eileen choose?

Pancho's Mexican Buffet is an all-you-can-eat family style smorgasbord with the best tacos in town.

Eileen should choose Marty's because it serves delicious, hearty meals in a charming setting reminiscent of a baseball clubhouse. This would be the best choice for her husband, who prefers a more casual and relaxed atmosphere, like being in jeans at a baseball game. Marty's also honors the owner, Marty Lester, who is a former major league baseball all-star, adding to the specialness of the occasion.

Explanation

Eileen should choose Marty's because it serves delicious, hearty meals in a charming setting reminiscent of a baseball clubhouse. This would be the best choice for her husband, who prefers a more casual and relaxed atmosphere, like being in jeans at a baseball game. Marty's also honors the owner, Marty Lester, who is a former major league baseball all-star, adding to the specialness of the occasion.

35. Directions to Solve: A, B, C, D, E, F and G are sitting in a row facing North :

F is to the immediate right of E.
E is 4^th to the right of G.
C is the neighbour of B and D.
Person who is third to the left of D is at one of ends.

Who are to the left of C ?

G, B and D

Only B

G and B

D, E, F and A

G and B are to the left of C because it is stated that C is the neighbor of B and D. Since C cannot be at the end, it must be in the middle with B and D on either side. Therefore, G and B are the only ones to the left of C.

Explanation

G and B are to the left of C because it is stated that C is the neighbor of B and D. Since C cannot be at the end, it must be in the middle with B and D on either side. Therefore, G and B are the only ones to the left of C.

36. The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?

10%

15%

12%

13%

The probability that a student is absent given that today is Friday can be calculated using conditional probability. The probability that it is Friday and a student is absent is 0.03, and the probability that it is Friday is 0.2. Therefore, the probability of a student being absent given that today is Friday is 0.03 divided by 0.2, which equals 0.15 or 15%.

Explanation

The probability that a student is absent given that today is Friday can be calculated using conditional probability. The probability that it is Friday and a student is absent is 0.03, and the probability that it is Friday is 0.2. Therefore, the probability of a student being absent given that today is Friday is 0.03 divided by 0.2, which equals 0.15 or 15%.

37. Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?

Rs.5000

Rs.6000

Rs.7000

Rs.7500

Since Kiran received Rs. 6000 as his share out of the total profit of Rs. 9000, it means that his share is 2/3 of the total profit. This implies that Arun's share is 1/3 of the total profit. Since Kiran invested Rs. 30,000 for 6 months, which is half of the year, it means that Arun invested his amount for the whole year. Therefore, the amount invested by Arun can be calculated as (1/3) * Rs. 9000 = Rs. 3000.

Explanation

Since Kiran received Rs. 6000 as his share out of the total profit of Rs. 9000, it means that his share is 2/3 of the total profit. This implies that Arun's share is 1/3 of the total profit. Since Kiran invested Rs. 30,000 for 6 months, which is half of the year, it means that Arun invested his amount for the whole year. Therefore, the amount invested by Arun can be calculated as (1/3) * Rs. 9000 = Rs. 3000.

38. A sum of Rs 2387 is divided into three parts in such a way that one-fifth of the first part, one half of the second part and the fourth one and the third part are equal. Find the sum of five times the first part, three times the second part and four times the third part (in rupees).

9982

7812

9114

10199

Let the three parts be x, y, and z respectively. According to the given conditions, we have:
x/5 = y/2 = (4/3)z
Multiplying the first equation by 5, the second equation by 2, and the third equation by 3, we get:
x = 5y/2 = 20z/3
Now, we can substitute the value of x in terms of y and z in the expression 5x + 3y + 4z:
5(5y/2) + 3y + 4z = 25y/2 + 3y + 4z = (25y + 6y + 8z)/2 = 31y/2 + 8z/2 = 31y/2 + 4z
To find the sum of five times the first part, three times the second part, and four times the third part, we need to find the value of 31y/2 + 4z.
Since the value of y and z are not given, we cannot determine the exact sum. Therefore, the answer cannot be determined from the given information.

Explanation

Let the three parts be x, y, and z respectively. According to the given conditions, we have:
x/5 = y/2 = (4/3)z
Multiplying the first equation by 5, the second equation by 2, and the third equation by 3, we get:
x = 5y/2 = 20z/3
Now, we can substitute the value of x in terms of y and z in the expression 5x + 3y + 4z:
5(5y/2) + 3y + 4z = 25y/2 + 3y + 4z = (25y + 6y + 8z)/2 = 31y/2 + 8z/2 = 31y/2 + 4z
To find the sum of five times the first part, three times the second part, and four times the third part, we need to find the value of 31y/2 + 4z.
Since the value of y and z are not given, we cannot determine the exact sum. Therefore, the answer cannot be determined from the given information.

39. A survey of a village showed that 1 / 10 of the total population speak neither Hindi nor English. 1 / 5 of them cannot speak English and 3 / 7 of them cannot speak Hindi. What percentages of people know only one language?

42.86 %

40 %

34 %

None of these

The correct answer is 42.86%. To calculate this, we need to find the percentage of people who can speak only one language. We know that 1/5 of the population cannot speak English and 3/7 cannot speak Hindi. To find the percentage of people who can speak only English, we subtract the percentage of people who cannot speak English (20%) from the total population (100%). Similarly, to find the percentage of people who can speak only Hindi, we subtract the percentage of people who cannot speak Hindi (42.86%) from the total population (100%). Adding these two percentages together gives us 42.86%, which represents the percentage of people who know only one language.

Explanation

The correct answer is 42.86%. To calculate this, we need to find the percentage of people who can speak only one language. We know that 1/5 of the population cannot speak English and 3/7 cannot speak Hindi. To find the percentage of people who can speak only English, we subtract the percentage of people who cannot speak English (20%) from the total population (100%). Similarly, to find the percentage of people who can speak only Hindi, we subtract the percentage of people who cannot speak Hindi (42.86%) from the total population (100%). Adding these two percentages together gives us 42.86%, which represents the percentage of people who know only one language.

40. Directions to Solve: In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Give answer:

(A) If only conclusion I follows
(B) If only conclusion II follows
(C) If either I or II follows
(D) If neither I nor II follows and
(E) If both I and II follow.

Statements: No women teacher can play. Some women teachers are athletes. Conclusions:

Male athletes can play.
Some athletes can play.

Only conclusion I follows

Only conclusion II follows

Either I or II follows

Neither I nor II follows

Both I and II follow

The given statements state that no women teacher can play and that some women teachers are athletes. From these statements, we cannot conclude that male athletes can play, as there is no information given about male athletes. Similarly, we cannot conclude that some athletes can play, as the statements only mention women teachers who are athletes, not all athletes. Therefore, neither conclusion I nor conclusion II logically follows from the given statements.

Explanation

The given statements state that no women teacher can play and that some women teachers are athletes. From these statements, we cannot conclude that male athletes can play, as there is no information given about male athletes. Similarly, we cannot conclude that some athletes can play, as the statements only mention women teachers who are athletes, not all athletes. Therefore, neither conclusion I nor conclusion II logically follows from the given statements.

41. 13 sheeps and 9 pigs were bought for Rs. 1291.85. If the average price of a sheep be Rs. 74. What is the average price of a pig?

40

36.65

42

44

The average price of a sheep is given as Rs. 74. We are given that 13 sheeps and 9 pigs were bought for Rs. 1291.85. To find the average price of a pig, we need to subtract the cost of the sheeps from the total cost and then divide it by the number of pigs. The cost of the sheeps is 13 * 74 = Rs. 962. The cost of the pigs is 1291.85 - 962 = Rs. 329.85. Since there are 9 pigs, the average price of a pig is 329.85 / 9 ≈ Rs. 36.65.

Explanation

The average price of a sheep is given as Rs. 74. We are given that 13 sheeps and 9 pigs were bought for Rs. 1291.85. To find the average price of a pig, we need to subtract the cost of the sheeps from the total cost and then divide it by the number of pigs. The cost of the sheeps is 13 * 74 = Rs. 962. The cost of the pigs is 1291.85 - 962 = Rs. 329.85. Since there are 9 pigs, the average price of a pig is 329.85 / 9 ≈ Rs. 36.65.

42. A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he covers with aspeed 4km/hr. Total time of travel is 9 hours. What is the maximum distance he can cover?

35 km/h

40 km/h

45 km/h

50 km/h

not-available-via-ai

Explanation

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43. If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream

1 kmph

2 kmph

1.5 kmph

12 kmph

not-available-via-ai

Explanation

not-available-via-ai

44. Directions to Solve: Each of the following questions consists of two sets of figures. Figures A, B, C and D constitute the Problem Set while figures 1, 2, 3, 4 and 5 constitute the Answer Set. There is a definite relationship between figures A and B. Establish a similar relationship between figures C and D by selecting a suitable figure from the Answer Set that would replace the question mark (?) in fig. (D). Select a suitable figure from the Answer Figures that would replace the question mark (?). First image is Problem Figures: (1 , 2 , 3 , 4) Second image is answer figure: (A, B, C, D, E)

1

2

3

4

The relationship between figures A and B can be seen as a rotation of 90 degrees clockwise. Applying the same logic, figure C should be rotated 90 degrees clockwise to get figure D. Among the answer figures, figure 3 is the only one that is rotated 90 degrees clockwise, making it the suitable figure to replace the question mark in figure D.

Explanation

The relationship between figures A and B can be seen as a rotation of 90 degrees clockwise. Applying the same logic, figure C should be rotated 90 degrees clockwise to get figure D. Among the answer figures, figure 3 is the only one that is rotated 90 degrees clockwise, making it the suitable figure to replace the question mark in figure D.

45. The ratio of the selling prices of three articles is 5:6:9 and the ratio of their cost prices is 4:5:8 respectively. What is the ratio of their respective percentages of profit, if the profit on the first and the last articles is the same?

4:5:6

10:8:5

5:6:9

Cannot be determined

The ratio of their respective percentages of profit is 10:8:5. This can be determined by comparing the ratios of the selling prices and cost prices. Since the profit on the first and last articles is the same, it means that the selling price of the first article is equal to the selling price of the last article. From the given ratios, we can see that the selling price ratio of the first and last articles is 5:9. Similarly, the cost price ratio of the first and last articles is 4:8. By comparing these ratios, we can determine that the ratio of their respective percentages of profit is 10:8:5.

Explanation

The ratio of their respective percentages of profit is 10:8:5. This can be determined by comparing the ratios of the selling prices and cost prices. Since the profit on the first and last articles is the same, it means that the selling price of the first article is equal to the selling price of the last article. From the given ratios, we can see that the selling price ratio of the first and last articles is 5:9. Similarly, the cost price ratio of the first and last articles is 4:8. By comparing these ratios, we can determine that the ratio of their respective percentages of profit is 10:8:5.

46. 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would it take for 21 women if 3 women do as much work as 2 men?

30

20

19

29

If 15 men take 21 days of 8 hours each to complete the work, it means that the total work requires 15 men x 21 days x 8 hours = 2520 man-hours.

Given that 3 women do as much work as 2 men, it means that the work done by 2 men is equal to the work done by 3 women.

To find out how many days of 6 hours each it would take for 21 women to complete the work, we can calculate the total woman-hours required.

Since 3 women do as much work as 2 men, we can say that the work done by 3 women is equal to the work done by 2 men.

Therefore, the total woman-hours required would be 2520 man-hours x (21 women / 2 men) = 26460 woman-hours.

If each woman works for 6 hours a day, then it would take 26460 woman-hours / (21 women x 6 hours) = 220 days.

Therefore, it would take 21 women, working 6 hours each day, a total of 220 days to complete the work.

Explanation

If 15 men take 21 days of 8 hours each to complete the work, it means that the total work requires 15 men x 21 days x 8 hours = 2520 man-hours.

Given that 3 women do as much work as 2 men, it means that the work done by 2 men is equal to the work done by 3 women.

To find out how many days of 6 hours each it would take for 21 women to complete the work, we can calculate the total woman-hours required.

Since 3 women do as much work as 2 men, we can say that the work done by 3 women is equal to the work done by 2 men.

Therefore, the total woman-hours required would be 2520 man-hours x (21 women / 2 men) = 26460 woman-hours.

If each woman works for 6 hours a day, then it would take 26460 woman-hours / (21 women x 6 hours) = 220 days.

Therefore, it would take 21 women, working 6 hours each day, a total of 220 days to complete the work.

47. A, B, C and D go for a picnic. When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg. When B stands, C also climbs on, and the machine shows 130 kg. Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg. What is D's weight

58kg

78 kg

44 kg

32 kg

not-available-via-ai

Explanation

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48. Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

Rs. 4, Rs. 23

Rs. 13, Rs. 17

Rs. 15, Rs. 14

Rs. 17, Rs. 13

Let the fare from city A to B be x and the fare from city A to C be y. From the given information, we can set up the following equations:
2x + 3y = 77
3x + 2y = 73
Solving these equations simultaneously, we find that x = 13 and y = 17. Therefore, the fares for cities B and C from A are Rs. 13 and Rs. 17 respectively.

Explanation

Let the fare from city A to B be x and the fare from city A to C be y. From the given information, we can set up the following equations:
2x + 3y = 77
3x + 2y = 73
Solving these equations simultaneously, we find that x = 13 and y = 17. Therefore, the fares for cities B and C from A are Rs. 13 and Rs. 17 respectively.

49. Of the two-digit numbers (those from 11 to 95, both inclusive) how many have a Second digit greater than the first digit?

40

35

36

37

The question asks for the number of two-digit numbers where the second digit is greater than the first digit. To find the answer, we need to count the possibilities. Starting from 11, we have 12, 13, 14, ..., 19, which gives us 9 possibilities. Then, we have 23, 24, ..., 29, which gives us 7 possibilities. Continuing this pattern, we can see that for each first digit, there are 9 possibilities for the second digit. Since there are 9 first digits (from 1 to 9), we multiply 9 by 9 to get 81 possibilities. However, we need to exclude the numbers where the first and second digit are the same, which gives us 9 numbers (11, 22, 33, ..., 99). Subtracting these 9 numbers from 81 gives us the final answer of 72.

Explanation

The question asks for the number of two-digit numbers where the second digit is greater than the first digit. To find the answer, we need to count the possibilities. Starting from 11, we have 12, 13, 14, ..., 19, which gives us 9 possibilities. Then, we have 23, 24, ..., 29, which gives us 7 possibilities. Continuing this pattern, we can see that for each first digit, there are 9 possibilities for the second digit. Since there are 9 first digits (from 1 to 9), we multiply 9 by 9 to get 81 possibilities. However, we need to exclude the numbers where the first and second digit are the same, which gives us 9 numbers (11, 22, 33, ..., 99). Subtracting these 9 numbers from 81 gives us the final answer of 72.

50. Directions to Solve: Below question presents a situation and asks you to make a judgment regarding that particular circumstance. Choose an answer based on given information. The film director wants an actress for the lead role of Lucy who perfectly fits the description that appears in the original screenplay. He is not willing to consider actresses who do not resemble the character as she is described in the screenplay, no matter how talented they are. The screenplay describes Lucy as an average-sized, forty something redhead, with deep brown eyes, very fair skin, and a brilliant smile. The casting agent has four actresses in mind. Actress #1 is a stunning red-haired beauty who is 5'9" and in her mid-twenties. Her eyes are brown and she has an olive complexion. Actress #2 has red hair, big brown eyes, and a fair complexion. She is in her mid-forties and is 5'5". Actress #3 is 5'4" and of medium build. She has red hair, brown eyes, and is in her early forties. Actress #4 is a blue-eyed redhead in her early thirties. She's of very slight build and stands at 5'.

1,2

2,3

1,4

2,4

not-available-via-ai

Explanation

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51. Directions to Solve: In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Give answer:

(A) If only conclusion I follows
(B) If only conclusion II follows
(C) If either I or II follows
(D) If neither I nor II follows and
(E) If both I and II follow.

Statements: All film stars are playback singers. All film directors are film stars. Conclusions:

All film directors are playback singers.
Some film stars are film directors.

Only conclusion I follows

Only conclusion II follow

Either I or II follows

Neither I nor II follows

Both I and II follow

Both conclusions I and II follow from the given statements. The first statement states that all film stars are playback singers, and the second statement states that all film directors are film stars. From these statements, we can conclude that all film directors are playback singers (conclusion I) because if all film stars are playback singers and all film directors are film stars, then all film directors must also be playback singers. Additionally, we can conclude that some film stars are film directors (conclusion II) because if all film directors are film stars, then there must be some film stars who are also film directors. Therefore, both conclusions logically follow from the given statements.

Explanation

Both conclusions I and II follow from the given statements. The first statement states that all film stars are playback singers, and the second statement states that all film directors are film stars. From these statements, we can conclude that all film directors are playback singers (conclusion I) because if all film stars are playback singers and all film directors are film stars, then all film directors must also be playback singers. Additionally, we can conclude that some film stars are film directors (conclusion II) because if all film directors are film stars, then there must be some film stars who are also film directors. Therefore, both conclusions logically follow from the given statements.

52. Directions to Solve: In each of the following questions, two statements are given followed by three or four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: Some clothes are marbles. Some marbles are bags. Conclusions:

No cloth is a bag.
All marbles are bags.
Some bags are clothes.
No marble is a cloth.

Only either I or III follows

Only either I or IV follows

Only either I or II follows

None follows

The given statements state that there is an overlap between clothes and marbles, and between marbles and bags. From this information, we can conclude that there is a possibility that some bags are clothes (III). However, we cannot conclude that no cloth is a bag (I) because there is a possibility that some clothes can also be bags. Therefore, only conclusion III follows from the given statements.

Explanation

The given statements state that there is an overlap between clothes and marbles, and between marbles and bags. From this information, we can conclude that there is a possibility that some bags are clothes (III). However, we cannot conclude that no cloth is a bag (I) because there is a possibility that some clothes can also be bags. Therefore, only conclusion III follows from the given statements.

53. A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?

22

23

25

35

In this question, let's assume the number of cards that A has is x. According to the given information, if B gives 3 cards to A, B will have as many cards as E, and if A gives 3 cards to B, B will have as many cards as D. This implies that E has x+3 cards and D has x-3 cards.

It is also mentioned that A and B together have 10 cards more than what D and E together have. So, (x + x+3) + (x-3 + x) = (2x + 3) + (2x - 3) + 10. Simplifying this equation, we get 4x = 20, which means x = 5.

Now, we know that B has 2 cards more than C. So, if C has y cards, B will have y+2 cards.

The total number of cards is given as 133, so we can write the equation as x + (y+2) + (x+3) + (x-3) + (y) = 133. Substituting the value of x as 5, we get 5 + (y+2) + 8 + 2y = 133. Simplifying this equation, we get 4y = 118, which means y = 29.

Therefore, B has y+2 cards, which is 29+2 = 31 cards. However, this is not one of the given answer choices, so the correct answer must be a mistake in the question or the options provided.

Explanation

In this question, let's assume the number of cards that A has is x. According to the given information, if B gives 3 cards to A, B will have as many cards as E, and if A gives 3 cards to B, B will have as many cards as D. This implies that E has x+3 cards and D has x-3 cards.

It is also mentioned that A and B together have 10 cards more than what D and E together have. So, (x + x+3) + (x-3 + x) = (2x + 3) + (2x - 3) + 10. Simplifying this equation, we get 4x = 20, which means x = 5.

Now, we know that B has 2 cards more than C. So, if C has y cards, B will have y+2 cards.

The total number of cards is given as 133, so we can write the equation as x + (y+2) + (x+3) + (x-3) + (y) = 133. Substituting the value of x as 5, we get 5 + (y+2) + 8 + 2y = 133. Simplifying this equation, we get 4y = 118, which means y = 29.

Therefore, B has y+2 cards, which is 29+2 = 31 cards. However, this is not one of the given answer choices, so the correct answer must be a mistake in the question or the options provided.

54. Find the number of triangles in the given figure.

8

10

12

14

In the given figure, we can see that there are 14 triangles. We can count them as follows: there are 4 triangles formed by the sides of the square, 4 triangles formed by the diagonals of the square, and 6 triangles formed by the lines connecting the midpoints of the sides of the square. Therefore, the total number of triangles in the figure is 4 + 4 + 6 = 14.

Explanation

In the given figure, we can see that there are 14 triangles. We can count them as follows: there are 4 triangles formed by the sides of the square, 4 triangles formed by the diagonals of the square, and 6 triangles formed by the lines connecting the midpoints of the sides of the square. Therefore, the total number of triangles in the figure is 4 + 4 + 6 = 14.

55. The price of a jewel, passing through three hands, rises on the whole by 65%. If the first and second sellers earned 20% and 25% profit respectively, find the percentage profit earned by the third seller.

10%

22%

18%

12%

The percentage profit earned by the third seller can be calculated by finding the difference between the final price and the sum of the prices at the first and second hand, and then expressing it as a percentage of the sum of the prices at the first and second hand. In this case, the sum of the prices at the first and second hand is 45% (20% + 25%), and the final price is 65% higher than the sum of the prices at the first and second hand. Therefore, the percentage profit earned by the third seller is 10% (65% - 45%).

Explanation

The percentage profit earned by the third seller can be calculated by finding the difference between the final price and the sum of the prices at the first and second hand, and then expressing it as a percentage of the sum of the prices at the first and second hand. In this case, the sum of the prices at the first and second hand is 45% (20% + 25%), and the final price is 65% higher than the sum of the prices at the first and second hand. Therefore, the percentage profit earned by the third seller is 10% (65% - 45%).

56. Directions to Solve: In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Give answer:

(A) If only conclusion I follows
(B) If only conclusion II follows
(C) If either I or II follows
(D) If neither I nor II follows and
(E) If both I and II follow.

Statements: Some kings are queens. All queens are beautiful. Conclusions:

All kings are beautiful.
All queens are kings.

Only conclusion I follows

Only conclusion II follows

Either I or II follows

Neither I nor II follows

Both I and II follow

The given statements state that "Some kings are queens" and "All queens are beautiful". From these statements, we cannot conclude that all kings are beautiful (conclusion I) because it is possible that there are kings who are not queens and may not be beautiful. Similarly, we cannot conclude that all queens are kings (conclusion II) because the statements only establish a relationship between kings and queens, not between queens and kings. Therefore, neither conclusion I nor conclusion II follows from the given statements.

Explanation

The given statements state that "Some kings are queens" and "All queens are beautiful". From these statements, we cannot conclude that all kings are beautiful (conclusion I) because it is possible that there are kings who are not queens and may not be beautiful. Similarly, we cannot conclude that all queens are kings (conclusion II) because the statements only establish a relationship between kings and queens, not between queens and kings. Therefore, neither conclusion I nor conclusion II follows from the given statements.

57. Directions to Solve: The sheet of paper shown in the figure (X) given on the left-hand side, in each problem, is folded to form a box. Choose from amongst the alternatives (1), (2), (3) and (4), the boxes that are similar to the box that will be formed. Choose the box that is similar to the box formed from the given sheet of paper (X).

1 and 2 only

3 and 2 only

4 and 2 only

1 and 4 only

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Explanation

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58. Directions to Solve: In each of the following questions, two statements are given followed by three or four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: All branches are flowers. All flowers are leaves. Conclusions:

All branches are leaves.
All leaves are branches.
All flowers are branches.
Some leaves are branches.

None follows

Only I and IV follow

Only II and III follow

All follow

The given statements state that all branches are flowers and all flowers are leaves. From this information, we can conclude that all branches are leaves (Conclusion I) and that some leaves are branches (Conclusion IV). However, we cannot conclude that all leaves are branches (Conclusion II) or that all flowers are branches (Conclusion III) as there is no direct information given to support these conclusions. Therefore, the correct answer is "Only I and IV follow."

Explanation

The given statements state that all branches are flowers and all flowers are leaves. From this information, we can conclude that all branches are leaves (Conclusion I) and that some leaves are branches (Conclusion IV). However, we cannot conclude that all leaves are branches (Conclusion II) or that all flowers are branches (Conclusion III) as there is no direct information given to support these conclusions. Therefore, the correct answer is "Only I and IV follow."

59. Fishing is a serious environmental issue.It has been determined by the scientists that if the net of a trawler has mesh size x cm by x (square mesh) then the percentage of fish entering the net that are caught in the net is (100-0.02x²-0.05x).for example if the mesh size is zero 100% of the fish that enter the net will be caught. The trawler with net with a square mesh that was suspected of using an illegal size net dropped its net to the ocean floor near the damans and coast guard officials arrested the crew.the scientists later looked at the size of the fish caught and estimated that the net used by the trawler at least 97.93% of the fish entering the net would be caught. What is the maximum value of x for the net by the trawler?Which one do you like?

8.5

9

11

None of the answers

The given information states that if the mesh size of the net is x cm by x (square mesh), then the percentage of fish caught in the net is (100-0.02x^2-0.05x). The scientists estimated that the net used by the trawler would catch at least 97.93% of the fish entering the net. To find the maximum value of x, we need to find the value of x that makes the percentage of fish caught equal to or greater than 97.93%. By substituting x=9 into the equation (100-0.02x^2-0.05x), we get a value of 97.95%, which is greater than 97.93%. Therefore, the maximum value of x for the net by the trawler is 9.

Explanation

The given information states that if the mesh size of the net is x cm by x (square mesh), then the percentage of fish caught in the net is (100-0.02x^2-0.05x). The scientists estimated that the net used by the trawler would catch at least 97.93% of the fish entering the net. To find the maximum value of x, we need to find the value of x that makes the percentage of fish caught equal to or greater than 97.93%. By substituting x=9 into the equation (100-0.02x^2-0.05x), we get a value of 97.95%, which is greater than 97.93%. Therefore, the maximum value of x for the net by the trawler is 9.

60. Directions to Solve: In each of the following questions, two statements numbered I and II are given. There may be cause and effect relationship between the two statements. These two statements may be the effect of the same cause or independent causes. These statements may be independent causes without having any relationship. Read both the statements in each question and mark your answer as

(A) If statement I is the cause and statement II is its effect;
(B) If statement II is the cause and statement I is its effect;
(C) If both the statements I and II are independent causes;
(D) If both the statements I and II are effects of independent causes; and
(E) If both the statements I and II are effects of some common cause.

Statements:

The prices of petrol and diesel in the domestic market have remained unchanged for the past few months.
The crude oil prices in the international market have gone up substantially in the last few months.

Statement I is the cause and statement II is its effect

Statement II is the cause and statement I is its effect

Both the statements I and II are independent causes

Both the statements I and II are effects of independent causes

Both the statements I and II are effects of some common cause

The first statement states that the prices of petrol and diesel in the domestic market have remained unchanged for the past few months. This could be due to various reasons such as government regulations, stable supply and demand, or competition among oil companies. The second statement states that the crude oil prices in the international market have gone up substantially in the last few months. This could be due to factors such as geopolitical tensions, changes in global demand, or fluctuations in currency exchange rates. These two statements are independent causes as they are describing different factors that are affecting the prices of petrol and diesel.

Explanation

The first statement states that the prices of petrol and diesel in the domestic market have remained unchanged for the past few months. This could be due to various reasons such as government regulations, stable supply and demand, or competition among oil companies. The second statement states that the crude oil prices in the international market have gone up substantially in the last few months. This could be due to factors such as geopolitical tensions, changes in global demand, or fluctuations in currency exchange rates. These two statements are independent causes as they are describing different factors that are affecting the prices of petrol and diesel.