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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:
65%
(hard)
Question Stats:
54% (01:39) correct
46%
(01:30)
wrong
based on 141
sessions
History
Date
Time
Result
Not Attempted Yet
Is 729 a member of set S?
(1) The first 20 positive integers are members of set S.
(2) Product of ANY two members of the set S, provided that the value of the product is less than 1000, is a member of the set S.
(1) The first 20 positive integers are members of set S.
(2) Product of ANY two members of the set S, provided that the value of the product is less than 1000, is a member of the set S.
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General Discussion
31 Dec 2021, 20:24
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Bunuel
Prime factorisation of 729 gives us 9*9*9
(1) The first 20 positive integers are members of set S.
Case1: There are only 20 positive integers in the set starting from 1. So 729 docent exists.
Case2: There are first 800 positive integers in the set. In that case 729 exists.
Yes and No both are possible.
Not Sufficient
(2) Product of ANY two members of the set S, provided that the value of the product is less than 1000, is a member of the set S.
Case1:Let there are first 81 positive integers in the set then 81*9 = 729 exists.
Case2:Let there be only 2 integers in the set 3 and 2 so set will have values as 3,2 and 6. 729 dose not exists.
Yes and No both are possible.
Not Sufficient.
Combining A and B
Case1: There are only 20 positive integers in the set starting from 1. So 729 dosen't exists. |in first 20 positive integers we won't get 3 9's on multiplying any two integers.
Case2:Let there are first 81 positive integers in the set then 81*9 = 729 exists.
Yes and No both still exists.
Not Sufficient
E is the answer.
