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A certain car's price decreased by 2.5% (from the original price) each

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A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 21 Jun 2016, 03:06
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Question Stats:

44% (02:05) correct 56% (02:27) wrong based on 190 sessions

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A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100

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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 21 Jun 2016, 04:50
1996 to 2002 = 6 years
in one year depreciation is 2.5% (note from original price)
which is $550
in 6 years total depreciation = 550*6 =$3300
increase in car price = $1500
car price in 2002 = 22000+1500-3300= $20200
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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 21 Jun 2016, 09:34
1
Bunuel wrote:
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100


Important point to notice- 2.5% decrease from the original price

2.5% of 22,000= 550

Total reduction in 6 years= 550*6= 3300

Final price= 22,000 +1500 - 3300= 20,200

C is the answer
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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 22 Jun 2016, 03:19
Bunuel wrote:
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100


Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500

Net price of the car in 02 = 18700 + 1500 = $20200

Correct Option: C
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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 22 Jun 2016, 04:26
Bunuel wrote:
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100



Reduction: 2.5 % from original price

(2.5/100) * 22000 = 550.

6 * 550 = Rs. 3300 reduction.

Increase: Rs, 1500

Final price: 22000 - 3300 + 1500 = 22000 - 1800 = 20200.

C is the answer.
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A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 12 Aug 2016, 16:57
Unless i am not reading the question properly, it is not mentioned that we have to use simple interest AND NOT COMPOUND interest. Am i overthinking?
I did following:
Final Price = P(1-r/100)^t
= 22000(1-25/1000)^7
= 22000(1-1/40)^7
= 22000 (1 - 7/40) Binomial short-cut
= 22000*33/40
= 550*33 = 11*50*3*11 = 121*150 = 18150
Adding cost to final price = 18150+1500 = 19650 => thus B

So in exam, like here (SC - focusing on similarity :lol: ), if it is not mentioned SI or CI we should use SI?
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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 01 Oct 2016, 08:33
1
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $1,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?

A. $18,400
B. $19,500
C. $20,200
D. $20,400
E. $21,100
---------------------------------------------------
Number of years from 1996 to 2002 = 6
Price of the car in 1996 = $22,000
Price decreased each year by 2.5%

We know that the price decreased 6 times @ 2.5% each year as the number of years from 1996 to 2002 is 6
Therefore, in place of going for lengthy and complicated calculation just multiply 2.5 with 6 -
2.5 * 6 = 15
Now, calculate 15% of $22,000
15/100 * 22,000 = $3300
Price of the car after decreasing the price for continuous 6 years @ 2.5%
= Price of Car in year 1996 (Initial Price) - Price decreased in 6 years
= $22,000 - $3300
= $18700

It is mentioned that the car's price increased by $1,500 with the investment in a new carburetor and a new audio system for the car
therefore, the final price of the car in year 2002 is -
= $18,700 + 1,500
= $20,200

Answer is 'C'
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Re: A certain car's price decreased by 2.5% (from the original price) each  [#permalink]

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New post 07 Sep 2018, 06:36
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Re: A certain car's price decreased by 2.5% (from the original price) each &nbs [#permalink] 07 Sep 2018, 06:36
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