M03-24

This question sparked something for me.. can fractions be considered even or odd? For example in statement 1 what if x were negative? So lets say n=4 and x=-2. I assume we don't consider 1/16 to be even since when divided by 2 it does not produce an integer?

Thanks!

If \(n\) is a positive integer, is \(n^x\) an even number?

(1) \(n\) is an even number. If \(x=0\) then \(n^x=1=\text{odd}\) but if \(x=1\) then \(n^x=n=\text{even}\). Not sufficient.

(2) \(x^2-3x+2 = 0\). Either \(x=1\) or \(x=2\). Not sufficient, since no info about \(n\).

(1)+(2) Since given that \(n=\text{even}\) then both \(n^1\) and \(n^2\) will be even. Sufficient.


Answer: C


It is given that (in the question stem) n is a positive integer, that means n>0
Now, if S1 specifies that, n is also even, that means n>1
Thus, eg: 2^x where x irrespective of being odd or even is still going to leave n^x as even

On solving S2 we get S as either 1 or 2. Thus, insufficient

And, I arrived at answer as A

Kindly let me know how do I guard against such ambiguity, of what is specified in the question stem vs the Statements. I mean should I consider statements independent of the question stems or Should question stems stand as true come what may.

Thanks, Pls correct me if I am wrong.