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