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Over the course of a year, a certain house appreciated in value by 10

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Over the course of a year, a certain house appreciated in value by 10  [#permalink]

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New post 30 Aug 2016, 05:16
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Over the course of a year, a certain house appreciated in value by 10 percent while the house next door decreased in value by 10 percent as a result of foundation damage. At the end of the year, the reduced price of the second house was what percentage of the increased price of the first house?

(1) The amount by which the first house increased in value was half as much as the amount by which the second house decreased in value.
(2) At the end of the year, the second house was worth $70,000 more than the first house.

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Re: Over the course of a year, a certain house appreciated in value by 10  [#permalink]

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New post 30 Aug 2016, 07:03
ANSWER: A (1) alone is sufficient; it allows you to infer that the initial value of the second house was twice that of the first house, so if x is the initial value of the first house and y is the initial value of the second house, y can be expressed as 2x. At the end of the year, the ratio of revised values of the second house to the first was 1.8x:1.1x; which can be expressed as a percentage as 164 percent. (2) alone is insufficient, because there are many values of both houses for which the statement could be true.
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Re: Over the course of a year, a certain house appreciated in value by 10  [#permalink]

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New post 30 Aug 2016, 20:18
Bunuel wrote:
Over the course of a year, a certain house appreciated in value by 10 percent while the house next door decreased in value by 10 percent as a result of foundation damage. At the end of the year, the reduced price of the second house was what percentage of the increased price of the first house?

(1) The amount by which the first house increased in value was half as much as the amount by which the second house decreased in value.
(2) At the end of the year, the second house was worth $70,000 more than the first house.


Let x becomes 1.1x after increase and
y becomes 0.9y after decrease in price

question : (0.9y/1.1x)*100 = ???

Statement 1: The amount by which the first house increased in value was half as much as the amount by which the second house decreased in value.

Amount of increase = 0.1x = (1/2)*(0.1y)
Now we have x/y which is required to answer the question. Hence,
SUFFICIENT

Statement 1: At the end of the year, the second house was worth $70,000 more than the first house.
0.9y = 70000+1.1x
But we can't determine the ration of x and y to answer the question Hence,
NOT SUFFICIENT

Answer: option A
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Re: Over the course of a year, a certain house appreciated in value by 10  [#permalink]

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New post 30 Aug 2016, 22:49
Bunuel wrote:
Over the course of a year, a certain house appreciated in value by 10 percent while the house next door decreased in value by 10 percent as a result of foundation damage. At the end of the year, the reduced price of the second house was what percentage of the increased price of the first house?

(1) The amount by which the first house increased in value was half as much as the amount by which the second house decreased in value.
(2) At the end of the year, the second house was worth $70,000 more than the first house.


A alone is sufficient to answer the questions.

Based on the condition X(1+10/100) and Y(1-10/100) are the new prices of houses.
The questions asks for second house price/first house price,

(Y(1-10/100)/X(1+10/100))

On reduction, this results in (9y/11x)....so we would be needing y/x to find out.

A) gives a ratio between x and y..so sufficient
B) y=x+70000...Multiple combo possible...so insuff.

A is the answer
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Re: Over the course of a year, a certain house appreciated in value by 10  [#permalink]

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New post 16 Oct 2017, 07:09
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Re: Over the course of a year, a certain house appreciated in value by 10 &nbs [#permalink] 16 Oct 2017, 07:09
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