microchip declines

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 5:35 am

The price of a microchip declines by 67 percent every six 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

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
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Source: Beat The GMAT — Problem Solving | Tue May 26, 2009 5:35 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Tue May 26, 2009 6:12 am

every 6 mnths the price becomes 37/100 of the previous price.
37/100~ 36/100 ~ 9/25 ~1/3

after 1 year price: 81*(1/3)^2=9
after 2 years price: 9*(1/3)^2=1

hence, B

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue May 26, 2009 6:25 am

I feel scoobydooby wanted to write 33/100 in place of 37/100, but cool approximation in the end.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: microchip declines

by Stuart@KaplanGMAT » Tue May 26, 2009 9:48 am

sanju09 wrote:The price of a microchip declines by 67 percent every six 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

Given that our number is divisible by 3, no need to approximate - quickest way will be brute force, multiplying by 1/3 each time (2/3 decrease = 1/3 of).

Start: 81
6 months: 27
1 year: 9
18 months: 3
2 years: 1

If we want to do it algebraically, the question is really asking:

If 81*(1/3)^x = 1, what's the value of x?

So, (1/3)^x = 1/81

1/(3^x) = 1/81
3^x = 81
x = 4

4*(6 months) = 2 years

Pick (b).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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