Series D(n) is such that i*D(i) = j*D(j) for any pair of positive integers (i, j). If D(1) is a positive integer, which of the following is possible?
I. 2*D(100) = D(99) + D(98)
II. D(1) is the only integer in the series
III. The series does not contain negative numbers	Choose the correct choice from the following
A) I only  B) II only  C) IIII only  D) IIIII only  E) I, IIIII
First thing I want to understand is this relation: i*D(i) = j*D(j) for any pair of positive integers. I will take examples to understand it.   When i = 1 and j = 2, D(1) = 2*D(2)   So D(2) = D(1)/2   When i = 1 and j = 3, D(1) = 3*D(3)   So D(3) = D(1)/3   I see it now. The series is: D(1), D(1)/2, D(1)/3, D(1)/4 and so on...   II and III are easily possible. We can see that without any calculations.   II. D(1) is the only integer in the series   If D(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except D(1)   III. The series does not contain negative numbers   Again, same series as above applies. In fact, since D(1) is a positive integer, this must be true.   I. 2*IIIII only(100) = IIIII only(99) + IIIII only(98)   2*IIIII only(1)/100 = IIIII only(1)/99 + IIIII only(1)/98 (cancel IIIII only(1) from both sides)   2/100 = 1/99 + 1/98   Not true hence this is not possible   Answer (IIIII only)
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Series D(n) is such that i*D(i) = j*D(j) for any pair of positive integers (i, j). If D(1) is a positive integer, which of the following is possible?
I. 2*D(100) = D(99) + D(98)
II. D(1) is the only integer in the series
III. The series does not contain negative numbers