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25 Apr 2020, 12:52
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Difficulty:
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Question Stats:
42% (02:01) correct
58%
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wrong
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Set A consists of the four integers x, \(x^{2}\) ,\(x^{3}\) and \(x^{4}\), and set B consists of the four integers x,2x,3x and 4x. What is the probability that a randomly selected integer from 1 to 100, inclusive, is a member of neither set A nor set B?
(1) \(x>5\)
(2) \(x<10\)
(1) \(x>5\)
(2) \(x<10\)
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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25 Apr 2020, 13:50
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Statement 1-
Case 1 - If x=6,
i) Only x and x^2 lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-5)/100
Case 2 - If x=11,
i) Only x lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-4)/100
Insufficient
Statement 2 -
Case 1 - If x=6,
i) Only x and x^2 lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-5)/100
Case 2 - If x=3,
i) x, x^2, x^3 and x^4 all lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-6)/100
Insufficient
Combining both statements
x= 6,7,8 or 9
i) x and x^2 all lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
and only x is common in 2 sets
Probability = (100-5)/100
Sufficient
Case 1 - If x=6,
i) Only x and x^2 lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-5)/100
Case 2 - If x=11,
i) Only x lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-4)/100
Insufficient
Statement 2 -
Case 1 - If x=6,
i) Only x and x^2 lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-5)/100
Case 2 - If x=3,
i) x, x^2, x^3 and x^4 all lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
Probability = (100-6)/100
Insufficient
Combining both statements
x= 6,7,8 or 9
i) x and x^2 all lies in the range from 1-100 in set A.
ii) x,2x,3x and 4x all lies in the range from 1-100 in set B.
and only x is common in 2 sets
Probability = (100-5)/100
Sufficient
Ravixxx
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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