Re: The sequence a1, a2, a3, ..., an of n integers is such that ak = k if
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29 May 2011, 12:24
I'll take a shot at explaining ...
If k is odd we know all the values are +ve and are equal to k (e.g. 1,3,5,7...)
If k is even we know all the values are -ve and are equal to the value of the prior term (e.g. a2 = -1,a4=-3... so the values will be, -1,-3,-5,-7 ....)
1, -1, 3, -3, 5, -5 .....
So as you can see at this point we know that for every value of k (when odd) we have a -ve value from when K is even, unless N (total terms) is odd in which case we will have one extra +ve term that will not cancel out. So if we have even number terms we know the result will be 0 (which is not positive). Therefore to get a positive sum we need one extra odd term.
Try it out,
N=5
1, -1, 3, -3, 5 (if add them, everything cancels out except 5, which is positive).
N=6
1, -1, 3, -3, 5, -5 (if add them, everything cancels out, result is not positive).
So, before looking at the statements we are able to rephrase the question to: "Is the number terms in the sequence odd?"
Statement 1: Gives us exactly that, therefore sufficient.
Statement 2: Well, it gives the same thing but instead of saying the number of terms is odd, it says the last term is +ve, which means the same thing as per our sequence above, there sufficient.
Answer D.
I hope this helps and makes sense.