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DIRECTIONS for questions: Select the correct alternative from the given choices.
There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?
- a)The weight of the student is greater than the initial average weight of either group.
- b)The weight of the student is less than the initial average weight of either group.
- c)The weight of the student is less than the initial average weight of group Q but greater than the initial average.
- d)The weight of the student is less than the average weight of group P but greater than the average weight of group Q.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
DIRECTIONS for questions: Select the correct alternative from the giv...
Let the average weights of students in groups P and Q be p and q respectively. Total weights of students in groups P and Q are 20p and 30q respectively. Let the weight of the student who shifted from group P to group Q be w. After the shifting of the student,
the average weights of groups P and Q become 20p – w / 19 and 30q + w / 31respectively.
Given that20p – w / 19< p.="" hence="" w="" /> p.
Also given that 30q + w / 31> q. Hence w > q.
Alternative Solution
If a higher-average group joins or a lower-average group leaves, the average increases.
If a lower-average group joins or a higher-average group leaves, the average decreases.
The student leaves P and the average decreases. Therefore the student’s weight is more than initial (as well as the final) average weight of P. He joins Q and the average increases. Therefore, the student’s weight is more than the initial (as well as final) average weight of Q.
Most Upvoted Answer
DIRECTIONS for questions: Select the correct alternative from the giv...
Analysis:
Let's consider the initial average weight of group P as AP and the initial average weight of group Q as AQ. After one student from group P shifts to group Q, the number of students in group P becomes 19 and the number of students in group Q becomes 31. Let's assume the weight of the student who shifted from group P to group Q as X.
Case 1: The average weight of group P decreases
If the average weight of group P decreases, it means that the sum of weights of all students in group P after the student shifted is less than the sum of weights of all students in group P before the student shifted.
Sum of weights in group P after the student shifted = 19(AP - X)
Sum of weights in group P before the student shifted = 20(AP)
So, 19(AP - X) < />
19AP - 19X < />
-19X < />
Case 2: The average weight of group Q increases
If the average weight of group Q increases, it means that the sum of weights of all students in group Q after the student shifted is greater than the sum of weights of all students in group Q before the student shifted.
Sum of weights in group Q after the student shifted = 31(AQ + X)
Sum of weights in group Q before the student shifted = 30(AQ)
So, 31(AQ + X) > 30(AQ)
31AQ + 31X > 30AQ
X > -AQ/31
Conclusion:
From Case 1, we have -19X < />
From Case 2, we have X > -AQ/31
Since the student shifted from group P to group Q, the weight of the student is less than the initial average weight of group Q but greater than the initial average weight of group P.
Therefore, the correct option is c) The weight of the student is less than the initial average weight of group Q but greater than the initial average weight of group P.
Let's consider the initial average weight of group P as AP and the initial average weight of group Q as AQ. After one student from group P shifts to group Q, the number of students in group P becomes 19 and the number of students in group Q becomes 31. Let's assume the weight of the student who shifted from group P to group Q as X.
Case 1: The average weight of group P decreases
If the average weight of group P decreases, it means that the sum of weights of all students in group P after the student shifted is less than the sum of weights of all students in group P before the student shifted.
Sum of weights in group P after the student shifted = 19(AP - X)
Sum of weights in group P before the student shifted = 20(AP)
So, 19(AP - X) < />
19AP - 19X < />
-19X < />
Case 2: The average weight of group Q increases
If the average weight of group Q increases, it means that the sum of weights of all students in group Q after the student shifted is greater than the sum of weights of all students in group Q before the student shifted.
Sum of weights in group Q after the student shifted = 31(AQ + X)
Sum of weights in group Q before the student shifted = 30(AQ)
So, 31(AQ + X) > 30(AQ)
31AQ + 31X > 30AQ
X > -AQ/31
Conclusion:
From Case 1, we have -19X < />
From Case 2, we have X > -AQ/31
Since the student shifted from group P to group Q, the weight of the student is less than the initial average weight of group Q but greater than the initial average weight of group P.
Therefore, the correct option is c) The weight of the student is less than the initial average weight of group Q but greater than the initial average weight of group P.
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DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. 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 for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. 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 for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer?.
DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. 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 for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. 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 for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of DIRECTIONS for questions: Select the correct alternative from the given choices. There are 50 students divided into two groups, P and Q, with 20 and 30 students respectively. One student from group P shifts to group Q. If as a result of this, the average weight of group P decreases, while the average weight of group Q increases, which of the following holds true?a) The weight of the student is greater than the initial average weight of either group.b) The weight of the student is less than the initial average weight of either group.c) The weight of the student is less than the initial average weight of group Q but greater than the initial average.d) The weight of the student is less than the average weight of group P but greater than the average weight of group Q.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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