2005 AMC 10A Problem 6

Attempt Problem 6 of the 2005 AMC 10A 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 2005 AMC 10A solutions, or check the answer key.

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

The average (mean) of

20

numbers is

30,

and the average of

30

other numbers is

20.

What is the average of all

50

numbers?

23

24

25

26

27

An average multiplied by the count gives the total sum

Add the two totals, then divide by

50

The combined sum is

20 \cdot 30 + 30 \cdot 20 = 600 + 600

= 1200.

The average of all

50

numbers is

\dfrac{1200}{50} = 24.

Thus, the correct answer is B.

Problem 6 in other years