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

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06 Dec 2008, 17:17

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My GMAT book left out the answer to this one. If someone could help me out with an explanation that would be great. Thanks!

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) If 4 is not the source, then 4=a square or a cube of another member. Since the set only contains positive intergers, 2 will have to be that member. Hence, 8 is in S (2^3)

2) If 64 is in S, possible that 4 is the source, and hence 8 may not be in the set (4^2 =16, 4^3=64). or its also possible that 2 is the source, in which case 8 would be in S. Hence INSUFF.

S is a set of all positive integers x,y and z where y = x^2 and z = x^3 for differnt values of x. And y and z are the sources from x.

Clue 1, 4 is in the set and since it is not the source, 2 and 8 will not be in the S(if 2 is included in the set then 4 and 8 also must be included in the set and that makes 4 to be source). Self Sufficient.

Clue 2, 64 is in the set and since it is not the source, 4 and 8 will not be in the S(sqrt and cube root of 64 should not be in the S).

From either of clues, we can say that 8 will not be in the set 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?

If 64 is in and is not the source, then it is the square or a cube of a number in it. That would mean that 4 or 8 would have to be in. and if 4 is in and not the source , then wouldn't 2 have to be in too? So if 2 is in, 8 is in, and we needed to know that both 64 and 4 weren't the source...so the answer should be C

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?

If 64 is in and is not the source, then it is the square or a cube of a number in it. That would mean that 4 or 8 would have to be in. and if 4 is in and not the source , then wouldn't 2 have to be in too? So if 2 is in, 8 is in, and we needed to know that both 64 and 4 weren't the source...so the answer should be C

Statement 2 does not day anything about the number 4, so you cant assume its not the source. Since statement 1 is already seen as sufficient, and 2 is not (given the info for 64), you dont need to consider option C..