1963 AMC 12 Problem 11

Attempt Problem 11 of the 1963 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 1963 AMC 12 solutions, or check the answer key.

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

11.

The arithmetic mean of a set of

50

numbers is

38.

If two numbers of the set, namely

45

and

55,

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

38.5

37.5

37

36.5

36

Recover the original sum from the mean

Subtract

45+55

and divide by

48

The original sum is

50\cdot38=1900.

After removing

45+55=100,

the remaining sum is

1800,

so the new mean is

\frac{1800}{48}=37.5.

Thus, the correct answer is B.

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