The price of a microchip declines 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1 ?
A. 1.5
B. 2
C. 3
D. 13
E. 13.5
source: www.800score.com
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First thing to notice is the funny values for the initial and final valus of our chip: $81 and $1. Interestingly, 81 is the square of 9.
Now to the problem. Every half year, the price becomes about one third of its original value. When the price decreases 67%, it becomes 33% or one third of the original value. So, in one year one gets a 1/3 times 1/3 or 1/9 reduction. So it is quite easy to conclude that the price-reduction process will be finished in two years because: $81 * 1/9 (one year) * 1/9 (another year) actually leads to the final proce of $1. Thus, we should take option B.
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