1955 AMC 12 Problem 3

Attempt Problem 3 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).

If each number in a set of ten numbers is increased by

20,

the arithmetic mean (average) of the original ten numbers:

remains the same

is increased by

20

is increased by

200

is increased by

10

is increased by

2

Increasing all ten entries adds

10\cdot20

to their sum

The new total is still divided by

10

If the original sum is

S,

the new sum is

S+10\cdot20.

Hence the new mean is

\frac{S+200}{10}=\frac S{10}+20.

The mean is increased by

20.

Thus, the correct answer is B.

Problem 3 in other years