In $1991,$ the price of a house was $80\%$ of its original price. In $1992,$ the price of the house was $60\%$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Sep 23, 2020 5:36 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. $33 \frac13\%$
D. $40\%$
E. $60\%$

Answer: B

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Wed Sep 23, 2020 5:36 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: In $1991,$ the price of a house was $80\%$ of its original price. In $1992,$ the price of the house was \(60\%

by deloitte247 » Fri Sep 25, 2020 7:53 pm

Let original price = x
In 1991, price = 80% of x = 0.8x
In 1992, price = 60% of x = 0.6x
By what percent did the price of the house decreased from 1991 to 1992
$$\%decrease=\frac{0.8x-0.6x}{0.8x}\cdot\frac{100}{1}$$
$$\%decrease=\frac{0.2x}{0.8x}\cdot\frac{100}{1}=0.25\cdot100=25\%$$

Answer = option B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In $1991,$ the price of a house was $80\%$ of its original price. In $1992,$ the price of the house was \(60\%

by Scott@TargetTestPrep » Mon Sep 28, 2020 12:33 pm

Gmat_mission wrote: ↑
Wed Sep 23, 2020 5:36 am
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. $33 \frac13\%$
D. $40\%$
E. $60\%$

Answer: B

Solution:

We can let the original price of the house be 100 thousand dollars; thus, the price of the house was 80 thousand dollars in 1991 and 60 thousand dollars in 1992. Therefore, the percent change of the price of the house from 1991 to 1992 is:

(60 - 80)/80 x 100 = -1/4 x 100 = -25 percent

Thus, the percent decrease is 25 percent.

Answer: B

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