2024 AMC 12A Problems/Problem 5

Problem 5

A data set containing $20$ numbers, some of which are $6$ , has mean $45$ . When all the 6s are removed, the data set has mean $66$ . How many 6s were in the original data set?

$\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8$

Solution

Because the set has $20$ numbers and mean $45$ , the sum of the terms in the set is $45\cdot 20=900$ .

Let there be $s$ sixes in the set.

Then, the mean of this new set is $\frac{900-6s}{20-s}$ . Equating this expression to $66$ and solving yields $s=7$ , so we choose answer choice $\boxed{\textbf{(A) }7}$ .

Page

Toolbox

Search

2024 AMC 12A Problems/Problem 5

Problem 5

Solution