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Directions: Study the following information carefully and answer the question given below.
A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.
The following information is also known about the number of friends who participated in each activity:
(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.
(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.
(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.
(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.
(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.
(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.
(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.
(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.
(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.
What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?
Correct answer is '6'. Can you explain this answer?
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Most Upvoted Answer
Directions: Study the following information carefully and answer the q...
Analysis:
Given Information:
- Friends who went to Goa participated in playing cards and/or charades.
- Friends who stayed at home participated in charades and/or watching movies.
- Number of friends who played cards was 8 more than the number who participated in exactly two activities.
- Number of friends who played charades in Goa was 7 greater than the number who watched movies.
- Total number of friends who played charades was 21 more than the number who played cards.
- Sum of friends who played charades and watched movies was 66.
- Total number of friends who participated in exactly two activities was 21, which was 4 more than those who only played cards.
Solution:
Step 1: Determine Variables
Let:
- x = Number of friends who played cards.
- y = Number of friends who played charades in Goa.
- z = Number of friends who watched movies.
- w = Number of friends who participated in exactly two activities.
- a = Number of friends who only played cards.
Step 2: Translate Given Information
- "Number of friends who played cards was 8 more than the number who participated in exactly two activities": x = w + 8
- "Number of friends who played charades in Goa was 7 greater than the number who watched movies": y = z + 7
- "Total number of friends who played charades was 21 more than the number who played cards": y + z = x + 21
- "Sum of friends who played charades and watched movies was 66": z + y = 66
- "Total number of friends who participated in exactly two activities was 21, which was 4 more than those who only played cards": w = a + 4
Step 3: Solve the Equations
Solving the above equations, we get:
- x = 29, y = 37, z = 29, w = 12, a = 8
Step 4: Calculate the Difference
Number of friends who went to Goa = y + x = 37 + 29 = 66
Number of friends who stayed at home = z + a = 29 + 8 = 37
Therefore, the difference between the number of friends who went to Goa and stayed at home is 66 - 37 = 29.
Given Information:
- Friends who went to Goa participated in playing cards and/or charades.
- Friends who stayed at home participated in charades and/or watching movies.
- Number of friends who played cards was 8 more than the number who participated in exactly two activities.
- Number of friends who played charades in Goa was 7 greater than the number who watched movies.
- Total number of friends who played charades was 21 more than the number who played cards.
- Sum of friends who played charades and watched movies was 66.
- Total number of friends who participated in exactly two activities was 21, which was 4 more than those who only played cards.
Solution:
Step 1: Determine Variables
Let:
- x = Number of friends who played cards.
- y = Number of friends who played charades in Goa.
- z = Number of friends who watched movies.
- w = Number of friends who participated in exactly two activities.
- a = Number of friends who only played cards.
Step 2: Translate Given Information
- "Number of friends who played cards was 8 more than the number who participated in exactly two activities": x = w + 8
- "Number of friends who played charades in Goa was 7 greater than the number who watched movies": y = z + 7
- "Total number of friends who played charades was 21 more than the number who played cards": y + z = x + 21
- "Sum of friends who played charades and watched movies was 66": z + y = 66
- "Total number of friends who participated in exactly two activities was 21, which was 4 more than those who only played cards": w = a + 4
Step 3: Solve the Equations
Solving the above equations, we get:
- x = 29, y = 37, z = 29, w = 12, a = 8
Step 4: Calculate the Difference
Number of friends who went to Goa = y + x = 37 + 29 = 66
Number of friends who stayed at home = z + a = 29 + 8 = 37
Therefore, the difference between the number of friends who went to Goa and stayed at home is 66 - 37 = 29.
Community Answer
Directions: Study the following information carefully and answer the q...
Let us draw a Venn diagram
From statement (1):
⇒ (b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2):
⇒ (a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3):
⇒ (a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e (From equation (1): c = 8 + e)
⇒ a + f = 29 ... (3)
From statement (4):
⇒ (a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5):
⇒ b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1):
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7):
⇒ b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4):
⇒ b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9):
⇒ a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10):
⇒ a + f = 29
⇒ f = 29 - 11 = 18
Difference between the number of friends who went to Goa and the number of friends who stayed at home = (11 + 12 + 17) - (7 + 9 + 18) = 40 - 34 = 6
From statement (1):
⇒ (b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2):
⇒ (a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3):
⇒ (a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e (From equation (1): c = 8 + e)
⇒ a + f = 29 ... (3)
From statement (4):
⇒ (a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5):
⇒ b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1):
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7):
⇒ b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4):
⇒ b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9):
⇒ a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10):
⇒ a + f = 29
⇒ f = 29 - 11 = 18
Difference between the number of friends who went to Goa and the number of friends who stayed at home = (11 + 12 + 17) - (7 + 9 + 18) = 40 - 34 = 6
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Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer?
Question Description
Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer?.
Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer?.
Solutions for Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer?, a detailed solution for Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? has been provided alongside types of Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: Study the following information carefully and answer the question given below.A group of friends was discussing how they spent last weekend. Some of them went to Goa, while others stayed at home. All the friends who went to Goa participated in at least one of the two activities - playing cards and charades. All the friends who stayed at home participated in at least one of the two activities - playing charades and watching movies.The following information is also known about the number of friends who participated in each activity:(1) The number of friends who played cards was 8 more than the number of friends who participated in exactly two activities among the entire group of friends.(2) The number of friends who played charades among those who went to Goa was 7 greater than the number of friends who watched movies.(3) The total number of friends who played charades among the entire group of friends was 21 more than the number of friends who played cards.(4) The sum of the number of friends who played charades among the entire group of friends and the number of friends who watched movies was 66.(5) The total number of friends who participated in exactly two activities was 21, which was four more than the number of friends who participated only in playing cards.What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?Correct answer is '6'. Can you explain this answer? tests, examples and also practice CAT tests.
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