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S is a set of positive integers such that if integer x is a member of

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S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Aug 2017, 03:35
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75% (hard)

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42% (01:58) correct 58% (01:53) wrong based on 109 sessions

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S is a set of positive integers such that if integer x is a member of S, then both x^2 and x^3 are also in S. If the only member of S that is neither the square nor the cube of another member of S is called the source integer, is 8 in S?

(1) 4 is in S and is not the source integer.

(2) 64 is in S and is not the source integer.

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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Aug 2017, 09:07
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Statement 1: if 4 is there and it's not a source , then it must be square of 2, which is the source in this case. Thus cube of 2 i.e 8 is lap there.
Sufficient.

Statement 2: if 64 is tee and it's not the source, then either it can be 8,64 and 8^3

Or it can be 4,16 and 64.

Not sufficient.

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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Aug 2017, 09:19
The answer should be A. If 4 is in S and is not the source integer then 2 has to be in the set. If 2 is in the set then 2^3 has to be in the set.
2nd statement isn't sufficient because if 64 is in the set then either 4 or 8 can be in the set. If 4 is in the set then 8 will not be. Giving both yes and no.
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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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10 Sep 2017, 09:23
Bunuel, can you please elaborate 2nd statement?

I think if 64 is not a source integer, then 8 or 4 is in S. So 8 is in S.Sufficient. What I am missing here?
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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Sep 2017, 01:31
Mehemmed wrote:
Bunuel, can you please elaborate 2nd statement?

I think if 64 is not a source integer, then 8 or 4 is in S. So 8 is in S.Sufficient. What I am missing here?

You said it your self either 4 OR 8 is in S. If 4 is the source integer (64 = 4^3), then 8 is NOT in the set but if 8 is the source integer (64 = 8^2), then 8 IS in the set. Two differen answers, hence insufficient.
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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Sep 2017, 03:44
Bunuel wrote:
S is a set of positive integers such that if integer x is a member of S, then both x^2 and x^3 are also in S. If the only member of S that is neither the square nor the cube of another member of S is called the source integer, is 8 in S?

(1) 4 is in S and is not the source integer.

(2) 64 is in S and is not the source integer.

Given : S is a set of positive integers such that if integer x is a member of S, then both x^2 and x^3 are also in S.
DS : is 8 in S?

Statement 1 : 4 is in S and is not the source integer. i.e. 2^2 is there. So, 2^3 i.e. 8 will also be there.
SUFFICIENT

Statement 2: 64 is in S and is not the source integer. i.e. 4^3 is there . 4^2 and 4 will also be there. But we can't say anything about 8.
NOT SUFFICIENT

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Re: S is a set of positive integers such that if integer x is a member of  [#permalink]

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11 Sep 2017, 09:01
Bunuel wrote:
Mehemmed wrote:
Bunuel, can you please elaborate 2nd statement?

I think if 64 is not a source integer, then 8 or 4 is in S. So 8 is in S.Sufficient. What I am missing here?

You said it your self either 4 OR 8 is in S. If 4 is the source integer (64 = 4^3), then 8 is NOT in the set but if 8 is the source integer (64 = 8^2), then 8 IS in the set. Two differen answers, hence insufficient.

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Re: S is a set of positive integers such that if integer x is a member of   [#permalink] 11 Sep 2017, 09:01
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