1953 AMC 12 Problem 30

Attempt Problem 30 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

30.

A house worth $9000\$9000 is sold by Mr. AA to Mr. BB at a 10%10\% loss. Mr. BB sells the house back to Mr. AA at a 10%10\% gain. The result of the two transactions is:
Mr. AA breaks even
Mr. BB gains $900\$900
Mr. AA loses $900\$900
Mr. AA loses $810\$810
Mr. BB gains $1710\$1710
Answer: D
Concepts:percentageprofit and losstransactions
Small hint:
Find the price of each sale separately
Big hint:
The second 10%10\% is taken from the first sale price, not from $9000\$9000
Solution:
Mr. BB first pays 9000(0.90)=8100 9000(0.90)=8100 dollars. He then sells the house back for 8100(1.10)=89108100(1.10)=8910 dollars. Mr. AA receives $8100\$8100 and pays $8910,\$8910, so he loses $810.\$810.
Thus, the correct answer is D.
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