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Is 729 a member of set S?

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Is 729 a member of set S?  [#permalink]

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New post 18 Sep 2017, 09:58
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Question Stats:

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Is 729 a member of set S?
1) The first 20 +ve 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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Re: Is 729 a member of set S?  [#permalink]

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New post 18 Sep 2017, 19:22
2
ManishKM1 wrote:
Is 729 a member of set S?
1) The first 20 +ve 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.

Source: Expert's Global


Hi...

Let's see the statements..
1) 1st 20 +ive integers are members of set S.
We do not know if there are any other members too.
The statement does not say ONLY these 20 are there.
Insufficient
2) product of any two numbers of set is also there.
Nothing much..
If only 1,2,4 are there then it will not have any multiple of 3.. ans NO
If 3 and 9 are there all power of 3 will be there and 729=3^6.... Ans YES
Different answers
Insuff

Combined..
We know 3 and 9 are there so 27,81,243,729 will also be there
Ans YES
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is 729 a member of set S?  [#permalink]

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New post 19 Sep 2017, 03:48
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ManishKM1 wrote:
Is 729 a member of set S?
1) The first 20 +ve 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.

Source: Expert's Global


S1-No information about the other members.
Not sufficient.
S2-Not sufficient as nothing is known about the members.
Combining both, we see that 3^6=729 will be in the set, since multiplication of 3 and its multiples upto 20 integers will contain 3^6.
Hence sufficient.

Answer C.

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Re: Is 729 a member of set S?  [#permalink]

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New post 16 Aug 2018, 10:32
Can anyone explain the 2nd statement a little more?

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.
Product of 2 numbers... Which 2 numbers?
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Re: Is 729 a member of set S?  [#permalink]

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New post 16 Aug 2018, 10:42
1
aghosh54 wrote:
Can anyone explain the 2nd statement a little more?

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.
Product of 2 numbers... Which 2 numbers?


Any two numbers ..

So if the set has two numbers 2,3
Then other numbers will be 2,3,6,12,18,24,36,...
So if you pick 2 and 3, 2*3=6 is there
If you pick 3 and 6, 3*6=18 is there..

So even 18*24 will be there and so on
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is 729 a member of set S? &nbs [#permalink] 16 Aug 2018, 10:42
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