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# calculation

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16 Mar 2004, 11:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hi all,
The following was in PR test:
The avg. price of a new car increased 12% from 1980 to 1985 and increased 20% from 1985 to 1990. If avg. price was \$11000 in 1980, what was the avg. price of a new car in 1990.

Is there a easier way to calculate this:

new avg. price = ((1.12)^5*11,000)*(1.20)^5)

Thanks.

Last edited by asagem99 on 16 Mar 2004, 14:06, edited 1 time in total.
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16 Mar 2004, 12:17
Is the increase yearly? The question does not say so but you seem to assume that it is.

1.20 * (1.12 * 11000) = 14784
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16 Mar 2004, 12:22
Yes, Nidhi, you are correct. I assumed it is yearly but it is not as your answer matches with official answer. Thanks.
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16 Mar 2004, 19:59
asagem,

This is GMAT, and WE always try to find an easier an easier way to solve problems due to time contraints. I would split the calculations into two parts, first 5 years, and next 5 years. Without seeing the answer choices, not sure how close I'll be, but here it is. If you ever heard, there is a 'rule' of 72. Basically stating, that any value will double in n number of years, and you find n by divinding 72 and interest rate (yearly, for simplicity). So from the first part Id say that the car would be twice the price in 6 years (72/12), in five approximately, 1.75 times. so, 11k turns to 19.5k without having to do any written calculations:

Second part: at 20 percent interest, the car's price will double in 72/20=~ 3.5 years, so it will be =~42k, we have 1.5 years left for an annual increase of ~.1.2%, so the final price will be in the area of 47K .

Am I close? Hope this helps.
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16 Mar 2004, 23:53
What is the official answer to this????
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17 Mar 2004, 07:26
lvb9th, the question does not say the increase is yearly. I misunderstood and thought it is yearly. But your rule 72 does help in calculation requiring multiple yearly increases. Thanks.
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