MathDB
2020 Individual #12

Source:

May 1, 2022
2020 Individual

Problem Statement

Jane's mother bakes cookies for Jane to share with her 66 friends. When the cookies are evenly divided among the 77 children (Jane and her 66 friends), there is one cookie left over. Given that each child receives at least 11 cookie, and Jane's mother baked less than 100100 cookies, how many different numbers of cookies could Jane's mother have baked? For example, she could have baked 1515 cookies, because each child receives 22 cookies, with 11 left over.
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>11<spanclass=latexbold>(C)</span>14<spanclass=latexbold>(D)</span>15<spanclass=latexbold>(E)</span>17<span class='latex-bold'>(A) </span>9\qquad<span class='latex-bold'>(B) </span>11\qquad<span class='latex-bold'>(C) </span>14\qquad<span class='latex-bold'>(D) </span>15\qquad<span class='latex-bold'>(E) </span>17