vinnik wrote:

Series A(n) is such that i*A(i) = j*A(j) for any pair of positive integers (i, j). If A(1) is a positive integer, which of the following is possible?

I. 2*A(100) = A(99) + A(98)

II. A(1) is the only integer in the series

III. The series does not contain negative numbers

A) I only

B) II only

C) I & III only

D) II & III only

E) I, II & III

Will appreciate if anyone explains this question with an easy method.

Thanks & Regards

Vinni

First thing I want to understand is this relation: i*A(i) = j*A(j) for any pair of positive integers. I will take examples to understand it.

When i = 1 and j = 2, A(1) = 2*A(2)

So A(2) = A(1)/2

When i = 1 and j = 3, A(1) = 3*A(3)

So A(3) = A(1)/3

I see it now. The series is: A(1), A(1)/2, A(1)/3, A(1)/4 and so on...

II and III are easily possible. We can see that without any calculations.

II. A(1) is the only integer in the series

If A(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except A(1)

III. The series does not contain negative numbers

Again, same series as above applies. In fact, since A(1) is a positive integer, this must be true.

I. 2*A(100) = A(99) + A(98)

2*A(1)/100 = A(1)/99 + A(1)/98 (cancel A(1) from both sides)

2/100 = 1/99 + 1/98

Not true hence this is not possible

Answer (D)

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