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31 May 2019, 10:57
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Is integer \(n\) a natural number?
1) \(n^2-8\) is sequence of a natural number
2) \(n^3-7\) is cube of a natural number
1) \(n^2-8\) is sequence of a natural number
2) \(n^3-7\) is cube of a natural number
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01 Jun 2019, 07:46
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You will never see the phrase "natural number" in a GMAT question, since mathematicians disagree about whether to include zero in the set of natural numbers. GMAT questions always tell you whether they are talking about "positive integers" (which would exclude zero) or about "non-negative integers" (which would be the positive integers along with zero).
In any case, using Statement 2, nothing can equal zero anyway, so we can interpret 'natural number' to mean 'positive integer'. if n^3 - 7 is the cube of a positive integer, then clearly n^3 - 7 is positive, so n^3 itself is positive, since n^3 is larger than n^3 - 7. If n^3 is positive, n must be positive, and since we are told n is also an integer, that means n is a "natural number". So Statement 2 is sufficient (we could even demonstrate that n = 2, since 1^3 and 2^3 are the only positive cubes separated by 7, but that's unnecessary here).
Statement 1 is meaningless (a number cannot be a 'sequence') so I have no idea how to interpret it. Even if it means to say "square" instead of "sequence", the statements would be contradictory, so the question still would make no sense. I'd suggest using better resources for practice.
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