Selling price of a car

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Vincelauret: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Mar 13, 2015 11:07 pmFollowed by: 1 member

by Vincelauret » Tue Mar 24, 2015 8:22 am

Hi I'm stuck with this problem, could you help me?

On January 1st, the selling price of a car was $A. The price initially increased by X% on February 1st, and then decreased by X% on March 1st, which resulted in an overall decrease in the price of the car by $1,400. What would have been the overall decrease in price had the increase on February 1st and decrease on March 1st been by 2X%??
A. $1,400
B. $2,800
C. $4,200
D. $5,600
E. $11,200

thanks

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Source: Beat The GMAT — Problem Solving | Tue Mar 24, 2015 8:22 am

talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 amFollowed by: 1 member; Thanked: 8 times

by talaangoshtari » Tue Mar 24, 2015 8:41 am

First, let x equal to 25, and then solve for A

A(1.25)(.75)=1400, so A equals to 1493.

Then we have:

1493(1.5)(.5)=z
z=1120

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Mar 24, 2015 8:45 am

Vincelauret wrote:Hi I'm stuck with this problem, could you help me?

On January 1st, the selling price of a car was $A. The price initially increased by X% on February 1st, and then decreased by X% on March 1st, which resulted in an overall decrease in the price of the car by $1,400. What would have been the overall decrease in price had the increase on February 1st and decrease on March 1st been by 2X%??
A. $1,400
B. $2,800
C. $4,200
D. $5,600
E. $11,200

Test an EASY CASE.

Let A = $100 and x%=10%.

Resulting decrease for x% = 10%:
Price on February 1st = 100 + 10% of 100 = 110.
Price on March 1st = 110 - 10% of 110 = 99.
Decrease = 100-99 = 1.

Resulting decrease for 2x% = 20%:
Price on February 1st = 100 + 20% of 100 = 120.
Price on March 1st = 120 - 20% of 120 = 96.
Decrease = 100-96 = 4.

Note the RATIO of the resulting decreases.
When x% doubles to 2x%, the resulting decrease is FOUR TIMES AS GREAT.
In the posted problem, since x% yields a decrease of $1400, the resulting decrease yielded by 2x% = 4*1400 = 5600.

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Mar 24, 2015 8:50 am

talaangoshtari wrote:First, let x equal to 25, and then solve for A

A(1.25)(.75)=1400, so A equals to 1493.

Careful!
The expression in red represents the RESULTING PRICE of the car on March 1st.
But $1400 is the DECREASE in the price of the car.
Thus, the equation above is not valid.

Correct equation:
Let A = the original price of the car and X = 25%.
Since the price on February 1st increases by 1/4, the price on February 1st = (5/4)A.
Since the price on March 1st decreases by 1/4, the price on March 1st = (3/4)(5/4)A = (15/16)A.
Resulting decrease = A - (15/16)A = (1/16)A.
Since the resulting decrease = 1400, we get:
(1/16)A = 1400
A = 22,400.

Resulting decrease for 2x% = 50%:
Price on February 1st = 22,400 + 50% of 22,400 = 33,600.
Price on March 1st = 33,600 - 50% of 33,600 = 16,800.
Resulting decrease = 22,400 - 16,800 = 5600.

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