The price of a microchip declines by 67 percent every 6 months. At thi

Question

The price of a microchip declines by 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 years 
B. 2 years 
C. 3 years 
D. 13 years 
E. 13.5 years

this is how i did it-

81- 67% * 81 = 27 approx
27 - 0.67*27 = 9 approx
9- 0.67*9 = 3 approx
3-0.67*3= $1 approx

hence, 24 months = 2 yrs

is there a faster way??

dahcrap · Accepted Answer

I think the fastest way is 

81 *(1/3)^n = 1
n =4
So 2 yrs

Himalayan · Answer

not sure whether you like this:

81 - (81 x 67%) / 3 = 81 - (81 x 2) / 3 = 27 = 81 / 3

1 = 81 / (3x3x3x3) = 81 / 3^4

so the time = 4 x 6 months = 24 months or 2 years.

r019h · Answer

i think it should be safe to use 60% (2/3) instead of 67% since the question says approximately.....that will reduce time spent....

r019h · Answer

not getting this part though-

 81 - (81 x 67%) / 3 = 81 - (81 x 2) / 3 = 27 = 81 / 3 <--why did you replace the 67% with 2??

wudy · Answer

You are right. 
I thought Himalayan made a typo. She tries to find out the leftover.
It should be "81 - (81 x 67%) = 81 - (81 x 2) / 3 = 27 = 81 / 3"

Himalayan · Answer

you guys are correct. 
there was a typo, it should be:

81 - (81 x 67%) = 81 - (81 x 2) / 3 = 27 = 81 / 3

ian7777 · Answer

Just divide 81 by 3 as many times as necessary to hit 1. It can't take more than 21 seconds to get the answer.

mbunny · Answer

i think the key to this question is notice that:

(1-67%) = 1-2/3 = 1/3

Then divide 81/3 until it hits 1.

EMPOWERgmatRichC · Answer

Hi All,

This question is really just about fractions and basic arithmetic, so you don't need a 'fancy' approach to solve it - you just need to do the necessary work on the pad.

We're told to start with an $81 microchip and that its price reduces by about 2/3 every 6 months. We're asked how long it takes for that chip to get to a $1 price. A few calculations should be all that's required to get to the answer:

Start: $81

Reducing this price by 2/3 means that 1/3 of the price will be left:
(1/3)(81) = 27
The price 6 months later is $27

We can repeat this same set of 'steps' again...
(1/3)(27) = 9
The price 12 months later is $9

(1/3)(9) = 3
The price 18 months later is $3

(1/3)(3) = 1
The price 24 months later is $1

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Temurkhon · Answer

(1/3)^x*81=1

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

x=4 and 4/2=2

B

DharLog · Answer

The price of a microchip declines by 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 years 
B. 2 years 
C. 3 years 
D. 13 years 
E. 13.5 years 
---------------------------

Like formula for deposit in the bank.

New Sum = Old sum * (1 + procent rate) exp (number of time periods)

N = O*(1+r)exp(n)
1 = 81 *(1-2/3)exp(n) (whre n is number of 6 month)
1/81 = (1/3)exp(n) -------------> n = 4 -------------> 2 years

danielarasan · Answer

You can solve this problem really fast if you recognize that to reduce 67% is te same as multiply by 1/3

81
81 * 1/3 = 27
27 * 1/3 = 9
9 * 1/3 = 3
3 * 1/3 = 1

So in 4 semesters you will reach 1 => 2 years!

Farina · Answer

What if we can't recognize 67% as 2/3 ?

EMPOWERgmatRichC · Answer

Hi Farina,

Even if you don't immediately recognize that 67% is approximately 2/3, then you can still get to the correct answer. Do you recognize that a 67% drop means that what remains is 33% of what you started with? And by extension, do you recognize that 33% is approximately 1/3? Any of those deductions creates math 'shortcuts' that you can use to save time.

If you didn't catch any of those patterns though, you would just have to do the math the 'long way' and do lots of Arithmetic...

What is 67% of $81?..... (.67)($81) = approximately $54.... so that 67% drop in price would make the cost of the microchip.... $81 - $54 = $27

What is 67% of $27?..... (.67)($27) = approximately $18.... so that next 67% drop in price would make the cost of the microchip.... $27 - $18 = $9

Etc.

Once you got down to $1, you'd have the number of 6-month 'periods' and you can answer the question.

GMAT assassins aren't born, they're made,
Rich

Farina · Answer

Thank you so much! 33% trick was a good one. Thanks a lot. God bless

adewale223 · Answer

1 = 81(1-2/3)^2x

1/81 = 1/3^2x

3^-4 = 3 ^-2x

-2x = -4

x = 2.

Posted from my mobile device

luisdicampo · Answer

Deconstructing the Question

The price declines by  67% every 6 months . 
So each period the price becomes:

33\% = 0.33 \approx \frac{1}{3}

Step-by-step

Start with:

81

After 6 months:

81 	imes \frac{1}{3} = 27

After 1 year:

27 	imes \frac{1}{3} = 9

After 1.5 years:

9 	imes \frac{1}{3} = 3

After 2 years:

3 	imes \frac{1}{3} = 1

Total periods:

4

Each period is  0.5 	ext{ years} :

4 	imes 0.5 = 2 	ext{ years}

Answer: 2 years

The price of a microchip declines by 67 percent every 6 months. At thi

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