Q) A series of positive numbers P1, P2, P3, …. Pn, Pn+1 = Pn/3 for all values of n ≥ 1. what is the value of 2P4?
(1) P2 = 1/3
(2) P2 - P3 = 2/9

OA is D
need some help in going about this type of problem.

Hey PudGe, again, according to forum guidelines, we need an original source for each question. Please provide and we're happy to help. :-)

_________________
Jamie Nelson
ManhattanGMAT Instructor

Hello Nelson,

This question is from the Mock test of Jamboree classes in India. This is from their free test, so It shouldn't be an issue to solve it.

This is a challenging question though...:p

Thanks,

Hi,

I believe the OA is D. Please correct me if I am wrong.

Hi,

The question does mention that Pn+1 = Pn/3 which is the equivalent of your statement. So I am unable to find anything wrong with the question. Could you please share what is wrong with the question. We do need the statements (each statement would suffice by itself) to provide us the first value of the expression.

Thanks krishnan! I get it now . . . any value in this sequence is the previous value divided by 3. This is an unusual way to express this and that is what threw me. Usually the testwriters would express this as Pn= P(n-1)/3.

_________________
Jamie Nelson
ManhattanGMAT Instructor

Okay, our first step is to define the formula for this series. As mentioned in my previous post, any value is obtained simply by taking the previous value and dividing that value by 3. That is what the P(n+1) = P(n)/3 means.

Okay, so if I want 2 * P(4), then I just need to know P(4) to be able to solve the question. Really, if I know any value in the sequence I could obtain P(4).

Statement 1 says that P(2) = 1/3. Sufficient. P(2) is 1/3, so P(3) is 1/9 (1/3 divided by 3). P(4) will be 1/9 divided by 3, or 1/27.

Statement 2 is only a little trickier:
Let's call P(2) = x
Because P(3) is P(2) divided by 3, P(3) = x/3.

Statement 2 says that P(2) - P(3) = 2/9. Thus x - x/3 = 2/9. 2/3x=2/9.
(3/2)2/3x = 2/9(3/2)
x=1/3
So we know that P(2) is 1/3. Sufficient.
Please note that we did not have to do much of this work for this statement. Once we had "x - x/3 = 2/9" we knew we could solve for x, which is standing in for P(2), and we should immediately have just said sufficient and moved on.

_________________
Jamie Nelson
ManhattanGMAT Instructor