1952 AMC 12 Problem 14

Attempt Problem 14 of the 1952 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 1952 AMC 12 solutions, or check the answer key.

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

14.

A house and store were sold for

\$12000

each. The house was sold at a loss of

20\%

of the cost, and the store at a gain of

20\%

of the cost. The entire transaction resulted in:

No loss or gain

Loss of

\$1000

Gain of

\$1000

Gain of

\$2000

None of these

Recover each original cost from its selling price separately

The house sold for

80\%

of cost, while the store sold for

120\%

of cost

The house cost

\frac{12000}{0.8}=15000

dollars, and the store cost

\frac{12000}{1.2}=10000

dollars. The combined cost was

25000

dollars, while the combined selling price was

24000

dollars, producing a loss of

1000

dollars.

Thus, the correct answer is B.

Problem 14 in other years