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Manager  Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 157
Schools: RD 2: Darden Class of 2012
The price of a certain property increased by 10% in the  [#permalink]

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12 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:41) correct 25% (01:40) wrong based on 287 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: 95
Re: Tuesday Q4 - House Values  [#permalink]

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1
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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
Joined: 29 Jun 2009
Posts: 157
Schools: RD 2: Darden Class of 2012
Re: Tuesday Q4 - House Values  [#permalink]

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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, 11:50.
Last edited by hogann on 13 Oct 2009, 17:53, edited 1 time in total.
Manager  Joined: 29 Jan 2011
Posts: 240
Re: Tuesday Q4 - House Values  [#permalink]

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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???
Manager  Joined: 29 Jan 2011
Posts: 240
Re: Tuesday Q4 - House Values  [#permalink]

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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.

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?
Retired Moderator B
Joined: 16 Nov 2010
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Re: Tuesday Q4 - House Values  [#permalink]

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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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Joined: 05 Mar 2015
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Re: The price of a certain property increased by 10% in the  [#permalink]

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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.

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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