Set Theory
Q.No: 1
Test Name : CAT Paper 2004
"Answer the questions on the basis of the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks."
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks."
If group B contains 23 questions, then how many questions are there in Group C?
Solution:
Q.No: 2
Test Name : CAT Paper 2004
"Answer the questions on the basis of the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks."
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks."
If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?
Solution:
Q.No: 3
Test Name : CAT Paper 2005
In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
Solution:
Q.No: 4
Test Name : CAT Paper 1991
Q 61 to 100 : Choose the best answer choice from those provided
Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?
Solution:
Q.No: 5
Test Name : CAT Paper 1991
Q 61 to 100 : Choose the best answer choice from those provided
Q.75 and 76 are based on the given data:
There were a hundred schools in a town. Of these, the number of schools having a play − ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
Q.75 and 76 are based on the given data:
There were a hundred schools in a town. Of these, the number of schools having a play − ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
How many schools had none of the three viz., laboratory, library or play − ground?
Solution:
Q.No: 6
Test Name : CAT Paper 1991
Q 61 to 100 : Choose the best answer choice from those provided
Let Y = minimum of {(x + 2), (3 − x)}. What is the maximum value of Y for
Solution:
Q.No: 7
Test Name : CAT Paper 1993
Q58 to 100 : Choose the appropriate answer choice.
Q69 and 70 : Use the following information :
Eighty five children went to an amusement park where they could ride on the merry go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
Q69 and 70 : Use the following information :
Eighty five children went to an amusement park where they could ride on the merry go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
How many children did not try any of the rides?
Solution:
Let x, y and z be the number of children who took 1 rides,
2 rides and 3 rides respectively.
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who did not try any of the rides = 85 (x + y + z) = 85 (15 + 35 + 20) = 15
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who did not try any of the rides = 85 (x + y + z) = 85 (15 + 35 + 20) = 15
Q.No: 8
Test Name : CAT Paper 1993
Q58 to 100 : Choose the appropriate answer choice.
Q69 and 70 : Use the following information :
Eighty five children went to an amusement park where they could ride on the merry go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
Q69 and 70 : Use the following information :
Eighty five children went to an amusement park where they could ride on the merry go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
How many children took exactly one ride?
Solution:
Let x, y and z be the number of children who took 1 rides,
2 rides and 3 rides respectively.
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who took exactly one ride = x = 15
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who took exactly one ride = x = 15
Q.No: 9
Test Name : CAT Paper 1993
Out of 100 families in the neighbourhood, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If 25 families have radio only, how many have only TV?
Solution:
Q.No: 10
Test Name : CAT Paper 1994
Q51 90 : Choose the best alternative.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Number of persons in Dighospur who read only Ganashakti is
Solution:
Q.No: 11
Test Name : CAT Paper 1994
Q51 90 : Choose the best alternative.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Number of persons in Aghosh Colony who read both of these newspapers is
Solution:
Q.No: 12
Test Name : CAT Paper 1994
Q51 90 : Choose the best alternative.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Q52 54 : are based on the following information:
Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur , Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; in his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.
Number of persons in Aghosh Colony who read only one paper
Solution:
Q.No: 13
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 103 and 104: Answer the questions on the basis of the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
What is the number of projects in which Gyani alone is involved?
Solution:
Putting the value of M in either equation, we get
G + B = 17.
Hence neither of two can be uniquely determined.
Hence neither of two can be uniquely determined.
Q.No: 14
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 103 and 104: Answer the questions on the basis of the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
What is the number of projects in which Medha alone is involved?
Solution:
Q.No: 15
Test Name : CAT Paper 2003 (L)
DIRECTIONS for Questions 126 to 150: Answer the questions independently of each other.
Let T be the set of integers {3, 11, 19, 27, , 451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is
Solution:
Tn = a + (n – 1)d
⇒ 467 = 3 + (n – 1)8
⇒ n = 59
Half of n = 29 terms
29th term is 227 and 30th term is 235 and when these.
two terms are added the sum is less than 470.
Hence the maximum possible values the set S can
have is 30.
⇒ 467 = 3 + (n – 1)8
⇒ n = 59
Half of n = 29 terms
29th term is 227 and 30th term is 235 and when these.
two terms are added the sum is less than 470.
Hence the maximum possible values the set S can
have is 30.
Q.No: 16
Test Name : CAT Paper 2003 (R)
Directions for questions 60 to 93: Answer the following questions independently.
Consider the sets Tn = {n, n +1, n + 2, n + 3, n + 4} , where n = 1, 2, 3, , 96. How many of these sets contain 6 or any integral multiple thereof (i.e. any one of the numbers 6, 12, 18, )?
Solution:
Q.No: 17
Test Name : CAT Paper 2003 (R)
Directions for questions 99 and 100: Answer the following questions independently.
A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options air conditioning, radio and power windows were already installed.
Following were the observation of the survey:
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?
Solution:
Q.No: 18
Test Name : CAT Paper 1990
N the set of natural numbers is partitioned into subsets S1 = (1), S2 = (2, 3), S3 ={4, 5, 6), S4 = {7, 8, 9, 10} and so on. The sum of the elements of the subset S50 is
Solution:
Q.No: 19
Test Name : CAT 2018 Actual Paper Slot 2
For two sets A and B, let AΔB denote the set of elements which belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (PΔQ)Δ(RΔS) is
Solution:
Q.No: 20
Test Name : CAT 2018 Actual Paper Slot 2
If A = {62n -35n -1: n = 1,2,3,...} and B = {35(n-1) : n = 1,2,3,...} then which of the following is true?
Solution:
Q.No: 21
Test Name : CAT 2019 Actual Paper Slot 1
A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is
Solution:
Q.No: 22
Test Name : CAT Actual Paper 2020 Slot-2
Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
Solution:
Q.No: 23
Test Name : CAT Actual Paper 2022 Slot-1
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
Solution:
Total = 100; coffee = 73
Tea = 80; Lemonade = 52
Max (all three) = 52
Min (all three) = 205 – 2 × 100 = 5
Required difference = 52 – 5 = 47.
Tea = 80; Lemonade = 52
Max (all three) = 52
Min (all three) = 205 – 2 × 100 = 5
Required difference = 52 – 5 = 47.
Q.No: 24
Test Name : CAT Actual Paper 2022 Slot-2
Question Numbers (25 to 29): Every day a widget supplier supplies widgets from the warehouse (W) to four locations
– Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each
location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis)
are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the
demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure
connecting the locations and warehouse represent two-way roads connecting those places with the distances (in
km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from
Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?
Solution:
Given that the last location is Ahmednagar, which means that the demand at A was the least among the four locations.
So the demand at A is 50. Then demand at B will be 60 and demand at D will be 50 (because these values cannot be less than the demand at A). Demand at C can be either 70 or 100, whichever be the case he will go from the warehouse to C first, thereby c traveling 12 km. From C he will go the the location with the next highest demand, which is B, thereby covering 4 km. Then he will go to D and cover (10 + 2 =) 12 km. Finally he will go to A, taking the path with the least distance, thereby covering (2 + 5 =) 7 km.
Total distance covered = 12 + 4 + 12 + 7 = 35 km.
Given that the last location is Ahmednagar, which means that the demand at A was the least among the four locations.
So the demand at A is 50. Then demand at B will be 60 and demand at D will be 50 (because these values cannot be less than the demand at A). Demand at C can be either 70 or 100, whichever be the case he will go from the warehouse to C first, thereby c traveling 12 km. From C he will go the the location with the next highest demand, which is B, thereby covering 4 km. Then he will go to D and cover (10 + 2 =) 12 km. Finally he will go to A, taking the path with the least distance, thereby covering (2 + 5 =) 7 km.
Total distance covered = 12 + 4 + 12 + 7 = 35 km.
Q.No: 25
Test Name : CAT Actual Paper 2022 Slot-2
Question Numbers (25 to 29): Every day a widget supplier supplies widgets from the warehouse (W) to four locations
– Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each
location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis)
are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the
demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure
connecting the locations and warehouse represent two-way roads connecting those places with the distances (in
km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from
Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?
Solution:
Given that the total number of widgets delivered is 250. The maximum possible number of widgets delivered can be 280 and the minimum possible number is 190. Note that 250 is 30 less than 280. Also the minimum and maximum demand in three out of four locations differ by 20 whereas in C it differs by 30. So the only possible way in which 250 widgets are delivered is:
A(70), B(6), C(70) and D(50). The first location visited is A, then C, Third is B and last location is D.
Distance covered = 5 + 5 + 12 + 4 + 10 + 2 = 38 km.
Given that the total number of widgets delivered is 250. The maximum possible number of widgets delivered can be 280 and the minimum possible number is 190. Note that 250 is 30 less than 280. Also the minimum and maximum demand in three out of four locations differ by 20 whereas in C it differs by 30. So the only possible way in which 250 widgets are delivered is:
A(70), B(6), C(70) and D(50). The first location visited is A, then C, Third is B and last location is D.
Distance covered = 5 + 5 + 12 + 4 + 10 + 2 = 38 km.
Q.No: 26
Test Name : CAT Actual Paper 2022 Slot-2
Question Numbers (25 to 29): Every day a widget supplier supplies widgets from the warehouse (W) to four locations
– Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each
location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis)
are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the
demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure
connecting the locations and warehouse represent two-way roads connecting those places with the distances (in
km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from
Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?
Solution:
Q.No: 27
Test Name : CAT Actual Paper 2022 Slot-2
Question Numbers (25 to 29): Every day a widget supplier supplies widgets from the warehouse (W) to four locations
– Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each
location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis)
are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the
demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure
connecting the locations and warehouse represent two-way roads connecting those places with the distances (in
km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from
Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?
Solution:
Q.No: 28
Test Name : CAT Actual Paper 2022 Slot-2
Question Numbers (25 to 29): Every day a widget supplier supplies widgets from the warehouse (W) to four locations
– Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each
location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis)
are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the
demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure
connecting the locations and warehouse represent two-way roads connecting those places with the distances (in
km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from
Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?
Solution:
Given that A is not the first location to be visited, this means that C is definitely visited first. The only route that will have a total distance of 29 km is C-B-A-D. The demand at C may be 100 or 70, at B it is 60, at A it is 50 and at D it may be 30 or 50. The total distance covered is 12 + 4 + 6 + 5 + 2 = 29 km. So the total number of widgets delivered can be 210, 230, 240 or 260.
Hence, 210 is a possible number of widgets that was delivered on that day.
Given that A is not the first location to be visited, this means that C is definitely visited first. The only route that will have a total distance of 29 km is C-B-A-D. The demand at C may be 100 or 70, at B it is 60, at A it is 50 and at D it may be 30 or 50. The total distance covered is 12 + 4 + 6 + 5 + 2 = 29 km. So the total number of widgets delivered can be 210, 230, 240 or 260.
Hence, 210 is a possible number of widgets that was delivered on that day.
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Let x, y and z be the number of children who took 1 rides,
2 rides and 3 rides respectively.
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who did not try any of the rides = 85 (x + y + z) = 85 (15 + 35 + 20) = 15
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who did not try any of the rides = 85 (x + y + z) = 85 (15 + 35 + 20) = 15
Solution:
Let x, y and z be the number of children who took 1 rides,
2 rides and 3 rides respectively.
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who took exactly one ride = x = 15
Since z = 20 and y + z = 55, y = 35.
Then, total number of rides = x + 2y + 3z = 145
⇒ x + 2 × 35 + 3 × 20 = 145
⇒ x = 15
Number of children, who took exactly one ride = x = 15
Solution:
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Putting the value of M in either equation, we get
G + B = 17.
Hence neither of two can be uniquely determined.
Hence neither of two can be uniquely determined.
Solution:
Solution:
Tn = a + (n – 1)d
⇒ 467 = 3 + (n – 1)8
⇒ n = 59
Half of n = 29 terms
29th term is 227 and 30th term is 235 and when these.
two terms are added the sum is less than 470.
Hence the maximum possible values the set S can
have is 30.
⇒ 467 = 3 + (n – 1)8
⇒ n = 59
Half of n = 29 terms
29th term is 227 and 30th term is 235 and when these.
two terms are added the sum is less than 470.
Hence the maximum possible values the set S can
have is 30.
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Total = 100; coffee = 73
Tea = 80; Lemonade = 52
Max (all three) = 52
Min (all three) = 205 – 2 × 100 = 5
Required difference = 52 – 5 = 47.
Tea = 80; Lemonade = 52
Max (all three) = 52
Min (all three) = 205 – 2 × 100 = 5
Required difference = 52 – 5 = 47.
Solution:
Given that the last location is Ahmednagar, which means that the demand at A was the least among the four locations.
So the demand at A is 50. Then demand at B will be 60 and demand at D will be 50 (because these values cannot be less than the demand at A). Demand at C can be either 70 or 100, whichever be the case he will go from the warehouse to C first, thereby c traveling 12 km. From C he will go the the location with the next highest demand, which is B, thereby covering 4 km. Then he will go to D and cover (10 + 2 =) 12 km. Finally he will go to A, taking the path with the least distance, thereby covering (2 + 5 =) 7 km.
Total distance covered = 12 + 4 + 12 + 7 = 35 km.
Given that the last location is Ahmednagar, which means that the demand at A was the least among the four locations.
So the demand at A is 50. Then demand at B will be 60 and demand at D will be 50 (because these values cannot be less than the demand at A). Demand at C can be either 70 or 100, whichever be the case he will go from the warehouse to C first, thereby c traveling 12 km. From C he will go the the location with the next highest demand, which is B, thereby covering 4 km. Then he will go to D and cover (10 + 2 =) 12 km. Finally he will go to A, taking the path with the least distance, thereby covering (2 + 5 =) 7 km.
Total distance covered = 12 + 4 + 12 + 7 = 35 km.
Solution:
Given that the total number of widgets delivered is 250. The maximum possible number of widgets delivered can be 280 and the minimum possible number is 190. Note that 250 is 30 less than 280. Also the minimum and maximum demand in three out of four locations differ by 20 whereas in C it differs by 30. So the only possible way in which 250 widgets are delivered is:
A(70), B(6), C(70) and D(50). The first location visited is A, then C, Third is B and last location is D.
Distance covered = 5 + 5 + 12 + 4 + 10 + 2 = 38 km.
Given that the total number of widgets delivered is 250. The maximum possible number of widgets delivered can be 280 and the minimum possible number is 190. Note that 250 is 30 less than 280. Also the minimum and maximum demand in three out of four locations differ by 20 whereas in C it differs by 30. So the only possible way in which 250 widgets are delivered is:
A(70), B(6), C(70) and D(50). The first location visited is A, then C, Third is B and last location is D.
Distance covered = 5 + 5 + 12 + 4 + 10 + 2 = 38 km.
Solution:
Solution:
Solution:
Given that A is not the first location to be visited, this means that C is definitely visited first. The only route that will have a total distance of 29 km is C-B-A-D. The demand at C may be 100 or 70, at B it is 60, at A it is 50 and at D it may be 30 or 50. The total distance covered is 12 + 4 + 6 + 5 + 2 = 29 km. So the total number of widgets delivered can be 210, 230, 240 or 260.
Hence, 210 is a possible number of widgets that was delivered on that day.
Given that A is not the first location to be visited, this means that C is definitely visited first. The only route that will have a total distance of 29 km is C-B-A-D. The demand at C may be 100 or 70, at B it is 60, at A it is 50 and at D it may be 30 or 50. The total distance covered is 12 + 4 + 6 + 5 + 2 = 29 km. So the total number of widgets delivered can be 210, 230, 240 or 260.
Hence, 210 is a possible number of widgets that was delivered on that day.
