MathDB

8

Part of 2022 AMC 10

Problems(2)

statistics moment

Source: 2022 AMC 10A #8 / 2022 AMC 12A #6

11/11/2022
A data set consists of 66 (not distinct) positive integers: 11, 77, 55, 22, 55, and XX. The average (arithmetic mean) of the 66 numbers equals a value in the data set. What is the sum of all positive values of XX?
<spanclass=′latex−bold′>(A)</span>10<spanclass=′latex−bold′>(B)</span>26<spanclass=′latex−bold′>(C)</span>32<spanclass=′latex−bold′>(D)</span>36<spanclass=′latex−bold′>(E)</span>40<span class='latex-bold'>(A) </span> 10 \qquad <span class='latex-bold'>(B) </span> 26 \qquad <span class='latex-bold'>(C) </span> 32 \qquad <span class='latex-bold'>(D) </span> 36 \qquad <span class='latex-bold'>(E) </span> 40
2022 AMC2022 AMC 10a2022 AMC 12AAMC 10AMC 12AMCarithmetic mean
2022 AMC 12B Problem 6

Source: 2022 AMC 10B # 8 / 2022 AMC 12B #6

11/17/2022
Consider the following 100100 sets of 1010 elements each: \begin{align*} &\{1,2,3,\cdots,10\}, \\ &\{11,12,13,\cdots,20\},\\ &\{21,22,23,\cdots,30\},\\ &\vdots\\ &\{991,992,993,\cdots,1000\}. \end{align*} How many of these sets contain exactly two multiples of 77?
<spanclass=′latex−bold′>(A)</span>40<spanclass=′latex−bold′>(B)</span>42<spanclass=′latex−bold′>(C)</span>43<spanclass=′latex−bold′>(D)</span>49<spanclass=′latex−bold′>(E)</span>50<span class='latex-bold'>(A)</span> 40\qquad<span class='latex-bold'>(B)</span> 42\qquad<span class='latex-bold'>(C)</span> 43\qquad<span class='latex-bold'>(D)</span> 49\qquad<span class='latex-bold'>(E)</span> 50
AMCAMC 122022 AMC2022 AMC 12BAMC 102022 AMC 10B