Problem Solving

eaakbari wrote:Enjoy..

The price of pens has increased over the years. Each year for the last 7 years the price has increased, and the new price is the sum of the prices for the two previous years. Last year a pen cost 60 rupees. How much does a pen cost today? How much did a pen cost 7 years ago?

This question could be reworded to be less ambiguous. Plus it would be nice to have some answer choices, since many GMAT questions can be solved by the process of elimination where we eliminate all but the correct choice.

That said, here's my approach:

Clarification: It sounds like the price was fixed for a few years. Let's say the price was p rupees during this period of fixed prices. Then, for 7 consecutive years, the price increased and the new (increased) price was the sum of the prices for the two previous years.

Fixed year: price = p
Fixed year: price = p
Fixed year: price = p . . . etc.
Year 1: price = 2p (note that this is the first year in which there's a price increase. Pemdas' solution includes 2 years in which there was no price increase)
Year 2: price = 3p
Year 3: price = 5p
Year 4: price = 8p
Year 5: price = 13p
Year 6: price = 21p
Year 7: price = 34p

Last year a pen cost 60 rupees.
So, in year 6, a pen cost 60 rupees.
This means that 21p = 60, which means p = 60/21 = 20/7 rupees

How much does a pen cost today?
In year 7 (today presumably), the price = 34p
So, the price = 34(20/7) = 680/7 rupees

How much did a pen cost 7 years ago? rupees
7 years ago, the price was p rupees.
So the price was 20/7 rupees

Cheers,
Brent