1951 AMC 12 Problem 5

Attempt Problem 5 of the 1951 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 1951 AMC 12 solutions, or check the answer key.

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

Mr.

A

owns a home worth

\$10{,}000.

He sells it to Mr.

B

at a

10\%

profit based on the worth of the house. Mr.

B

sells the house back to Mr.

A

at a

10\%

loss. Then:

A

comes out even

A

makes

\$1100

on the deal

A

makes

\$1000

on the deal

A

loses

\$900

on the deal

A

loses

\$1000

on the deal

Compute the two sale prices separately

The first sale is for

10{,}000(1.10)

, and the return sale is

10\%

below that amount

The first sale price is

10{,}000(1.10)=11{,}000.

The return sale is

11{,}000(0.90)=9{,}900.

Mr.

A

receives

11{,}000

and pays back

9{,}900,

so he gains

1{,}100.

Thus, the correct answer is B.

Problem 5 in other years