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18 Jan 2024, 07:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:42) correct
36%
(02:50)
wrong
based on 180
sessions
History
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Time
Result
Not Attempted Yet
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
A) $1,400
B) $2,800
C) $4,200
D) $5,600
E) $11,200
18 Jan 2024, 10:38
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Bunuel
OA is D
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Screenshot_20240118_230726_Samsung Notes.jpg [ 443.32 KiB | Viewed 3904 times ]
22 Jan 2024, 03:03
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Original scenario:
Jan: $A
Feb: increased by X% - A(1+X\100)
Mar: decreased by X% - (A+AX\100)(1-X\100) = A+AX\100-AX\100-AX^2\100 = A-AX^2\100
Overall decrease = 1400
A-(A-AX^2\100)=1400 = AX^2\100=1400
New scenario
Jan: $A
Feb: increased by 2X% - A(1+2X\100)
Mar: decreased by X% - (A+2AX\100)(1-2X\100) = A+2AX\100-2AX\100-4AX^2\100 = A-4AX^2\100
Overall decrease in new scenario:
A-(A-4AX^2\100) = 4AX^2\100
NOTE: That's 4 time the decrease of the original scenario.
1400*4 = 4000+1600=5600
Answer choice D.
Jan: $A
Feb: increased by X% - A(1+X\100)
Mar: decreased by X% - (A+AX\100)(1-X\100) = A+AX\100-AX\100-AX^2\100 = A-AX^2\100
Overall decrease = 1400
A-(A-AX^2\100)=1400 = AX^2\100=1400
New scenario
Jan: $A
Feb: increased by 2X% - A(1+2X\100)
Mar: decreased by X% - (A+2AX\100)(1-2X\100) = A+2AX\100-2AX\100-4AX^2\100 = A-4AX^2\100
Overall decrease in new scenario:
A-(A-4AX^2\100) = 4AX^2\100
NOTE: That's 4 time the decrease of the original scenario.
1400*4 = 4000+1600=5600
Answer choice D.
