2020 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2020 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 12A solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:percentagefraction

Difficulty rating: 840

1.

Carlos took 70%70\% of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left?

10%10\%

15%15\%

20%20\%

30%30\%

35%35\%

Solution:

After Carlos takes 70%,70\%, the remaining portion is 30%.30\%.

Maria takes one third of this, namely 1330%=10%,\tfrac13 \cdot 30\% = 10\%, leaving 30%10%=20%.30\% - 10\% = 20\%.

Thus, C is the correct answer.

Problem 1 in Other Years