1955 AMC 12 Problem 22

Attempt Problem 22 of the 1955 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 1955 AMC 12 solutions, or check the answer key.

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

22.

On a

\$10{,}000

order a merchant has a choice between three successive discounts of

20\%,

20\%,

and

10\%

and three successive discounts of

40\%,

5\%,

and

5\%.

By choosing the better offer, he can save:

nothing at all

\$440

\$330

\$345

\$360

Successive discounts multiply the remaining-price factors

Compare

0.8\cdot0.8\cdot0.9

with

0.6\cdot0.95\cdot0.95

The first offer leaves a fraction

0.8\cdot0.8\cdot0.9=0.576

of the price. The second leaves

0.6\cdot0.95^2=0.5415.

The second is cheaper by

0.576-0.5415=0.0345

of the order, or

0.0345(10000)=345

dollars.

Thus, the correct answer is D.

Problem 22 in other years