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Statement 1: S could be 10 and root 10 therefore is an irrational number. This means S is neither odd or even. S could also be 0.

Statement 2: S could be root 9. Also S could be 0.

!+2) Still could be 0 or a root number. If this is a GMAT question it will tell you if it's an integer or not. If it doesn't there are endless possibility that exist for numbers that match both of those statements.

Statement 1: S could be 10 and root 10 therefore is an irrational number. This means S is neither odd or even. S could also be 0.

Statement 2: S could be root 9. Also S could be 0.

!+2) Still could be 0 or a root number. If this is a GMAT question it will tell you if it's an integer or not. If it doesn't there are endless possibility that exist for numbers that match both of those statements.

Answer is E.

Isn't 0 an even integer? I agree with the explanation otherwise since integers have to be whole numbers with no decimals. I can see the answer is E. But when you say S can be 0, isn't \(s^2=0\) which is an even integer?
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"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

(1) \(\sqrt{s}\) is not an even integer. Notice we are not told that \(\sqrt{s}=odd\), we are told that \(\sqrt{s}\neq{even}\), those ARE NOT the same. \(\sqrt{s}\) might be an odd integer, for example 1, 3, ... and in this case \(s\) will be an odd integer, but \(\sqrt{s}\) might as well be a fraction, for example 1/3, 7/5 and in this case \(s\) won't be an integer at all. \(\sqrt{s}\) also might be an irrational number, for example \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{{\frac{1}{3}}}\) ... and in this case \(s\) might or might not be an odd integer. Not sufficient.

(2) \(s^2\) is not an even integer. Notice again that we are not told that \(s^2=odd\), we are told that \(s^2\neq{even}\), those ARE NOT the same. The same here: \(s^2\) might be a square of an odd integer, for example 1, 9, ... and in this case \(s\) will be an odd integer, but \(s^2\) might as well not be a perfect square, for example 1/3, 17, and in this case \(s\) won't be an integer at all. Not sufficient.

(1)+(2) When combined still insufficient: if \(s=1\) then the answer will be YES but if \(s=\frac{1}{3}\) then the answer will be NO.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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