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# The price of a certain property increased by 10% in the

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Manager
Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 173
Schools: RD 2: Darden Class of 2012
The price of a certain property increased by 10% in the  [#permalink]

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13 Oct 2009, 05:41
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25% (medium)

Question Stats:

77% (01:38) correct 23% (01:42) wrong based on 422 sessions

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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.
Manager
Joined: 12 Oct 2009
Posts: 99
Re: Tuesday Q4 - House Values  [#permalink]

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13 Oct 2009, 06:25
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hogann 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.

Both are sufficient
Let the price be X then at end of 1st year price is 1.1X (10% increase) then in 2nd year price become 0.88X(20% decrease) and in 3rd year price become 1.1X (25% increase). We need to find dollar decrease in price in second year
1. given at end of 3rd year price was \$22000 which is equal to 1.1X so X = \$20000. We can find dollar decrease hence A is suff
2. We know price at end of 2nd year was 0.88 X which is a decrease of 0.12X and increase in price in 3rd year = 1.1X -0.88X = 0.22X
so 0.22X - 0.12X = 2000. We get X and can asnwer for the question. Hence B is also suff

Manager
Affiliations: CFA Level 2 Candidate
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Re: Tuesday Q4 - House Values  [#permalink]

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Updated on: 13 Oct 2009, 16:53
2
[quote="asterixmatrix]

Both are sufficient
Let the price be X then at end of 1st year price is 1.1X (10% increase) then in 2nd year price become 0.88X(20% decrease) and in 3rd year price become 1.1X (25% increase). We need to find dollar decrease in price in second year
1. given at end of 3rd year price was \$22000 which is equal to 1.1X so X = \$20000. We can find dollar decrease hence A is suff
2. We know price at end of 2nd year was 0.88 X which is a decrease of 0.12X and increase in price in 3rd year = 1.1X -0.88X = 0.22X
so 0.22X - 0.12X = 2000. We get X and can asnwer for the question. Hence B is also suff

Great explanation!

Originally posted by hogann on 13 Oct 2009, 10:50.
Last edited by hogann on 13 Oct 2009, 16:53, edited 1 time in total.
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Joined: 29 Jan 2011
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Re: Tuesday Q4 - House Values  [#permalink]

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19 Jun 2011, 17:11
asterixmatrix wrote:

Both are sufficient
Let the price be X then at end of 1st year price is 1.1X (10% increase) then in 2nd year price become 0.88X(20% decrease) and in 3rd year price become 1.1X (25% increase). We need to find dollar decrease in price in second year
1. given at end of 3rd year price was \$22000 which is equal to 1.1X so X = \$20000. We can find dollar decrease hence A is suff
2. We know price at end of 2nd year was 0.88 X which is a decrease of 0.12X and increase in price in 3rd year = 1.1X -0.88X = 0.22X
so 0.22X - 0.12X = 2000. We get X and can asnwer for the question. Hence B is also suff

Let the price be X then at end of 1st year price is 1.1X (10% increase) then in 2nd year price become 0.88X(20% decrease)

How does 2nd year price become 0.88x shouldnt it be 1.1x - 0.2x = 0.9 x???
Senior Manager
Joined: 29 Jan 2011
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Re: Tuesday Q4 - House Values  [#permalink]

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19 Jun 2011, 17:18
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.

Can someone please tell me whats wrong with this approach=>

Let p denote the original price of the property

Price of property after 1st year = p + 10/100 p = 1.1p
Price of property after 2st year = 1.1p - 0.2p = 0.9 p <----- why is this 0.88 for all and 0.9 for me ?
Price of property after 3rd year = 0.9p + .25p = 1.15 p

Statement1:
1.15 p = 22,000 <----- why cant wer just substitute price of 3rd year equal to 22,000 ?

Therefore, p = 22000/1.15 ???

Why is this wrong?
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Re: Tuesday Q4 - House Values  [#permalink]

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19 Jun 2011, 20:33
1.1p - 0.2p = 0.9 p <----- why is this 0.88 for all and 0.9 for me ?

You should take as (1.1p - 0.2 * 1.1p), and not 0.2p, as the decrease is from the increased price - "1.1p", and not the original price p.

As for your second question, the correct equation can be framed as :

.15 p = 22,000 <----- why cant wer just substitute price of 3rd year equal to 22,000 ?

If p is the original price :

Price at 3rd year = 22000 = p(1+ 10/100) ( 1 - 20/100) ( 1 + 25/100)
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Re: The price of a certain property increased by 10% in the  [#permalink]

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12 Jun 2016, 11:25
hogann 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.

Although i get D as correct answer ,i m getting different values for both the statements.
(1) let initial price be P
P(11/10)(4/5)(5/4)=220000
P=200000.
(2) 3rd year-2nd year=2000

P(11/10)(4/5)(5/4)-P(11/10)(4/5)=2000
P(11/10)(4/5)(5/4-1)=2000
P(11/10)(4/5)(1/4)=2000
P=2000*200/44 = 400000/44.....

can anyone clear plz....
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Re: The price of a certain property increased by 10% in the  [#permalink]

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30 Mar 2018, 17:02
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Re: The price of a certain property increased by 10% in the   [#permalink] 30 Mar 2018, 17:02
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