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The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.
There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?
I. The probability that when 2 people are selected are random, both will be from same gender is 7/15
II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25
- a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.
- b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.
- c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
- d)Either statement alone is sufficient.
- e)Both statements together are not sufficient to answer the question.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The problem consists of a question followed by 2 statements. Check wh...
Let there be 'x' boys.
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Total number of people = 4 + x
From Statement I:
P(both will be from same gender)
= 1 - P(both are from different gender)
= 1 - P(1 boy, 1 girl)
= 1 - (xC1)(4C1)/(4+xC2)
= 1 - 4x/4 + x)(3 + x)/2)
= (x2 - x + 12)/(x2 + 7x + 12)
Given, (x2 - x + 12)/(x2 + 7x + 12) = 7/15
=> 15x2 - 15x + 180 = 7x2 + 49x + 84
=> x2 - 8x + 12 = 0
=> (x - 2)(x - 6) = 0
=> x = 2 or 6
So a unique value of the number of boys cannot be determined.
From Statement II:
P(2 people from opposite gender with replacement)
= P(1st is Boy, 2nd is girl) + P(1st is girl, 2nd is boy)
= (x/(4 + x*(4/(4 + x)) + (4/(4 + x))*(x/(4 + x))
= 8x/(4 + x)2
Given, 8x/(4 + x)2 = 12/25
=> 2x/(x2 + 8x + 16) = 3/25
=> 3x2 - 26x + 48 = 0
=> (x - 6)(3x - 8) = 0
=> x = 6 as x ≠ 8/3
So, Statement II alone is sufficient.
Most Upvoted Answer
The problem consists of a question followed by 2 statements. Check wh...
Problem Analysis:
The question asks for the number of boys who went for the picnic. We are given two statements to determine the answer. Let's analyze each statement individually.
Statement I: The probability that when 2 people are selected at random, both will be from the same gender is 7/15.
This statement tells us the probability of selecting two people of the same gender. However, it does not provide any information about the number of boys or girls specifically. Therefore, we cannot determine the number of boys who went for the picnic based on this statement alone.
Statement II: The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25.
This statement tells us the probability of selecting two people of opposite genders. Again, it does not provide any information about the number of boys or girls specifically. Therefore, we cannot determine the number of boys who went for the picnic based on this statement alone.
Combining the Statements:
Let's analyze both statements together to see if we can determine the number of boys who went for the picnic.
If we consider both statements together, we can infer the following:
- The probability of selecting two people of the same gender is 7/15.
- The probability of selecting two people of opposite genders is 12/25.
However, this information is still not sufficient to determine the number of boys who went for the picnic. We cannot determine the exact number of boys or girls, as the statements only provide information about the probabilities of selecting people of the same or opposite genders.
Therefore, neither statement alone nor both statements together are sufficient to answer the question.
Conclusion:
Based on the analysis, we can conclude that neither statement alone nor both statements together are sufficient to determine the number of boys who went for the picnic. Hence, the correct answer is option 'E' - Both statements together are not sufficient to answer the question.
The question asks for the number of boys who went for the picnic. We are given two statements to determine the answer. Let's analyze each statement individually.
Statement I: The probability that when 2 people are selected at random, both will be from the same gender is 7/15.
This statement tells us the probability of selecting two people of the same gender. However, it does not provide any information about the number of boys or girls specifically. Therefore, we cannot determine the number of boys who went for the picnic based on this statement alone.
Statement II: The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25.
This statement tells us the probability of selecting two people of opposite genders. Again, it does not provide any information about the number of boys or girls specifically. Therefore, we cannot determine the number of boys who went for the picnic based on this statement alone.
Combining the Statements:
Let's analyze both statements together to see if we can determine the number of boys who went for the picnic.
If we consider both statements together, we can infer the following:
- The probability of selecting two people of the same gender is 7/15.
- The probability of selecting two people of opposite genders is 12/25.
However, this information is still not sufficient to determine the number of boys who went for the picnic. We cannot determine the exact number of boys or girls, as the statements only provide information about the probabilities of selecting people of the same or opposite genders.
Therefore, neither statement alone nor both statements together are sufficient to answer the question.
Conclusion:
Based on the analysis, we can conclude that neither statement alone nor both statements together are sufficient to determine the number of boys who went for the picnic. Hence, the correct answer is option 'E' - Both statements together are not sufficient to answer the question.
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The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer?
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The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. 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 The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer?.
The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. 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 The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer?.
Solutions for The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The problem consists of a question followed by 2 statements. Check whether the statements are sufficient to answer the question. Choose the option accordingly.There are 4 girls and some boys who went for a Picnic, what is the number of Boys who went for the picnic?I. The probability that when 2 people are selected are random, both will be from same gender is 7/15II. The probability that when 2 people are picked one by one with replacement, both will be from opposite gender is 12/25a)Statement I alone is sufficient, but Statement II alone is not sufficient to answer the question.b)Statement II alone is sufficient, but Statement I alone is not sufficient to answer the question.c)Both statements taken together are sufficient to answer the question, but neither statement alone is sufficientd)Either statement alone is sufficient.e)Both statements together are not sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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