satishchandra wrote:If series A(n) is such that A(n) = A(n-1)/n, how many elements of the series are larger than 1/2?
(1) A(2) = 5
(2) A(1)-A(2) = 5
I think this problem stinks.
For one thing, A(n) is clearly supposed to be a recursively defined sequence, not a series. A series is the sum of the terms in a sequence; a sequence is, informally, a list of numbers. Maybe it doesn't seem like a big deal, but I'd have a hard time taking this source seriously if the writers can't be bothered to use correct terminology.
For another thing, this is a very poorly defined recursive sequence. The question provides no base case and does not explicitly say for which values of n the rule is applicable. So, when we look at statement 1, which says A(2)=5, we plug this in to the formula to get A(1)=10. Now, the existence of A(1) implies the existence of A(0) because we're told that A(n)=A(n-1)/n for the elements of this sequence, so we can say 10=A(0)/1, or A(0)=10. But the existence of A(0) is troubling, because if we plug THAT into the formula we get A(0)=A(-1)/0, which is undefined. So everything ultimately rests on something that's undefined.
To head off all this nonsense we need a statement that accompanies the rule such as "A(n)=A(n-1)/n for integers n>=1" or "n>=2". If the writers intended the former, then the starting term is A(0) and the sequence goes A0,A1,A2,A3,A4,...=10,10,5,5/3,5/12,... and there are 4 terms greater than 1/2. If they mean the latter, then the starting term is A1, and the sequence goes A1,A2,A3,A4,...=10,5,5/3,5/12,..., and there are 3 terms greater than 1/2.
So maybe all this is because the answer is E. However, I really don't think this kind of ambiguous ill-defined crap is the kind of thing GMAT questions are really supposed to be about. Plus, I'm told the OA is D.
So in conclusion, I would throw this source directly in the garbage can.
