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Property Price

by kanha81 » Mon May 11, 2009 10:27 am
The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
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Re: Property Price

by splendentsky » Mon May 11, 2009 11:51 am
kanha81 wrote:The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
I think D is the answer.

If we know the original price of this property, we can solve the amount of the dollar decrease during the second year.

Analysis:
Lets assume the original price of the property is 1 when he bought it.
Year 0 : 1
End of Year 1 : 1*(1+0.1)
= 1.1
End of Year 2 : 1.1*(1-0.2)
= 0.88
End of Year 3 : 0.88*(1+0.25)
= 1.1

Data 1:
Let x be the original price of the property. The end of year 3, the property worth 1.1 times of original price.
1.1 * x = 22,000
x = 20,000
We know the original price of the property, without further calculation, we know the $ decrease in the second year.
A itself is correct, we can eliminate C and E.

Data 2:
The decrease in the property price over the first two years = the increase in the property price during the third year - $2,000
The decrease in the property price over the first two years = 1 - 0.88
= 0.12
The increase in the property price during the third year = 1.1 - 0.88
= 0.22

Let's x be the original price of the property,
0.12 x = 0.22x - 2,000
x = 20,000

After we found original price, we can solve the question.

Hope this helps. :)
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Re: Property Price

by kanha81 » Tue May 12, 2009 9:33 am
splendentsky wrote:
kanha81 wrote:The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
I think D is the answer.

If we know the original price of this property, we can solve the amount of the dollar decrease during the second year.

Analysis:
Lets assume the original price of the property is 1 when he bought it.
Year 0 : 1
End of Year 1 : 1*(1+0.1)
= 1.1
End of Year 2 : 1.1*(1-0.2)
= 0.88
End of Year 3 : 0.88*(1+0.25)
= 1.1

Data 1:
Let x be the original price of the property. The end of year 3, the property worth 1.1 times of original price.
1.1 * x = 22,000
x = 20,000
We know the original price of the property, without further calculation, we know the $ decrease in the second year.
A itself is correct, we can eliminate C and E.

Data 2:
The decrease in the property price over the first two years = the increase in the property price during the third year - $2,000
The decrease in the property price over the first two years = 1 - 0.88
= 0.12
The increase in the property price during the third year = 1.1 - 0.88
= 0.22

Let's x be the original price of the property,
0.12 x = 0.22x - 2,000
x = 20,000

After we found original price, we can solve the question.

Hope this helps. :)
Excellent explanation indeed splendentsky! OA is [spoiler][D][/spoiler]

Any alternative ways that could suggest right away that (i) & (ii) are solvable?
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