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08 May 2017, 09:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (02:03) correct
39%
(01:58)
wrong
based on 200
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Set S of Cardinality of 7 has distinct elements. Is the probability of picking out a prime number from Set S less than 4/5?
(1)The least element and the largest element of Set S are 8 and 18 respectively
(2) If 2 prime elements are added into Set S, the probability that a prime number is picked up from the extended set S is 1/3
(1)The least element and the largest element of Set S are 8 and 18 respectively
(2) If 2 prime elements are added into Set S, the probability that a prime number is picked up from the extended set S is 1/3
abhijitatprepitt
08 May 2017, 10:57
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Tan2017
Cardinality 7 => the set has 7 elements (distinct).
A) least element is 8, largest is 18. So there are remaining 5 other elements. Maximum number of prime numbers possible between 8 and 18 is 3: 11, 13, 17. The maximum possible probability of picking a prime number from 7 numbers between 8 and 18 => 3/7 (Assuming all prime numbers between 8 and 18 are part of set S). 3/7 < 4/5 . Since the maximum possible probability is already less, we can answer YES to the question. Hence A is sufficient.
B) Lets say we have n prime numbers in the set. The initial probability will be n/7. Now we add two additional prime numbers to the set making it (n+2) prime numbers in a set of 9 elements. So new probability = (n+2)/9 . This new probability is given as equal to 1/3.
(n+2)/9 = 1/3 => n=1 => This means there is only 1 prime number in the set of 7 elements.
So initial probability: 1/7. Which is definitely less than 4/5. Answers YES to the asked question. Hence B is sufficient.
So answer (D) each statement individually is sufficient.
08 May 2017, 12:59
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I'd like to point out that the test-makers do not expect you to know the meaning of "cardinality"
On the official GMAT, the question would likely be worded as follows:
Set S contains 7 distinct numbers. Is the probability of randomly selecting a prime number from Set S less than 4/5?
Cheers,
Brent
On the official GMAT, the question would likely be worded as follows:
Set S contains 7 distinct numbers. Is the probability of randomly selecting a prime number from Set S less than 4/5?
Cheers,
Brent
