MathDB
Pairs :)

Source: 2022 AMC 10A #14 / 2022 AMC 12A #10

November 11, 2022
AMCAMC 102022 AMC 10a2022 AMC2022 AMC 12AAMC 12

Problem Statement

What is the number of ways the numbers from 11 to 1414 can be split into 77 pairs such that for each pair, the greater number is at least 22 times the smaller number?
<spanclass=latexbold>(A)</span>108<spanclass=latexbold>(B)</span>120<spanclass=latexbold>(C)</span>126<spanclass=latexbold>(D)</span>132<spanclass=latexbold>(E)</span>144<span class='latex-bold'>(A) </span>108\qquad<span class='latex-bold'>(B) </span>120\qquad<span class='latex-bold'>(C) </span>126\qquad<span class='latex-bold'>(D) </span>132\qquad<span class='latex-bold'>(E) </span>144