1971 AMC 12 Problem 16

Attempt Problem 16 of the 1971 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 1971 AMC 12 solutions, or check the answer key.

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

16.

After finding the average of

35

scores, a student carelessly included the average with the

35

scores and found the average of these

36

numbers. The ratio of the second average to the true average was:

1:1

35:36

36:35

2:1

None of these

Call the original average

x

The original sum is

35x

, and the extra number is also

x

If the true average is

x,

then the original sum is

35x.

Including

x

itself gives a sum of

36x

over

36

numbers, so the new average is still

x.

The ratio is

1:1.

Therefore, the correct answer is A.

Problem 16 in other years