1959 AMC 12 Problem 13

Attempt Problem 13 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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

13.

The arithmetic mean (average) of a set of

50

numbers is

38.

If two numbers, namely,

45

and

55,

are discarded, the mean of the remaining set of numbers is:

36.5

37

37.2

37.5

37.52

Concepts:mean

Recover the original sum from the mean and number of entries

Subtract

45+55

and divide by the

48

remaining entries

The original sum is

50\cdot38=1900.

After removing

45

and

55,

the remaining sum is

1800,

so the new mean is

\frac{1800}{48}=37.5.

Therefore, the correct answer is D.

Problem 13 in other years