2024 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

A data set containing

20

numbers, some of which are

6,

has mean

45.

When all the

6

s are removed, the data set has mean

66.

How many

6

s were in the original data set?

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Solution

The full set sums to

20\cdot45=900.

Removing

k

sixes leaves

20-k

numbers summing to

900-6k,

with mean

66,

900-6k=66(20-k)

=1320-66k.

Then

60k=420,

giving

k=7.

Thus, the correct answer is D.

Concepts: mean · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.