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In 1991, the price of a house was 80% of its original price.

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by BTGmoderatorDC » Mon Jan 07, 2019 2:05 am
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In 1991, the price of a house was 80% of its original price. In 1992, the price of the house was 60% of its original price. By what percent did the price of the house decrease from 1991 to 1992 ?

A. 20%
B. 25%
C. 33 1/3%
D. 40%
E. 60%

OA B

Source: Princeton Review
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by fskilnik@GMATH » Mon Jan 07, 2019 3:34 am
BTGmoderatorDC wrote:In 1991, the price of a house was 80% of its original price. In 1992, the price of the house was 60% of its original price. By what percent did the price of the house decrease from 1991 to 1992 ?

A. 20%
B. 25%
C. 33 1/3%
D. 40%
E. 60%
Source: Princeton Review
$$?\,\,\,:\,\,\,\Delta \% = \frac{{{P_{92}} - {P_{91}}}}{{{P_{91}}}}\,\,\,\,\,\,\,\left( {\Delta \% < 0} \right)$$
$$\left. \matrix{
{P_{91}} = {4 \over 5}P \hfill \cr
{P_{92}} = {3 \over 5}P\,\,\, \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\Delta \% = {{ - {1 \over 5}P} \over {{4 \over 5}P}} = - {1 \over 4}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 25\% \,\,{\rm{decrease}}$$

This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
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by GMATGuruNY » Mon Jan 07, 2019 5:03 am
BTGmoderatorDC wrote:In 1991, the price of a house was 80% of its original price. In 1992, the price of the house was 60% of its original price. By what percent did the price of the house decrease from 1991 to 1992 ?

A. 20%
B. 25%
C. 33 1/3%
D. 40%
E. 60%
Let the original price = 100.
1991 price = 80% of 100 = 80.
1992 price = 60% of 100 = 60.
Percent decrease from 80 to 60 = (Difference/Larger) * 100 = (20/80) * 100 = 25.

The correct answer is B.
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by swerve » Mon Jan 07, 2019 9:45 am
Let original price be 100$; so in 1991 price would be 80$ and 1992 60$, price decreased by (80-60)/80= 25% option B
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by Brent@GMATPrepNow » Mon Jan 07, 2019 9:58 am
BTGmoderatorDC wrote:In 1991, the price of a house was 80% of its original price. In 1992, the price of the house was 60% of its original price. By what percent did the price of the house decrease from 1991 to 1992 ?

A. 20%
B. 25%
C. 33 1/3%
D. 40%
E. 60%
I'd typically assign a "nice" value to the original price, and then follow the steps that Mitch demonstrated.
Alternatively, we can solve the question algebraically

In 1991, the price of a house was 80% of its original price.
Let x = the original price
So, 0.8x = the 1991 price

In 1992, the price of the house was 60% of its original price.
So, 0.6x = the 1992 price

By what percent did the price of the house decrease from 1991 to 1992 ?
Percent change = 100(change)/old
= 100(0.8x - 0.6x)/0.8x
= 100(0.2x)/0.8x
= 100(0.2)/0.8
= 25%

Answer: B

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by Scott@TargetTestPrep » Sun Jan 27, 2019 6:25 pm
BTGmoderatorDC wrote:In 1991, the price of a house was 80% of its original price. In 1992, the price of the house was 60% of its original price. By what percent did the price of the house decrease from 1991 to 1992 ?

A. 20%
B. 25%
C. 33 1/3%
D. 40%
E. 60%

OA B

Source: Princeton Review
If the original price is n, then in 1991, the price is 0.8n and in 1992 the price is 0.6n. The percent change is:

(0.6n - 0.8n)/0.8n x 100 = -2/8 x 100 = -25% (i.e., a 25% decrease)

Answer: B

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