MathDB

19

Part of 2022 MIG

Problems(2)

2022 A Individual #19

Source:

4/28/2022
A three-digit number NN is equal to 3636 times the sum of its digits. Find the sum of all possible values of NN.
<spanclass=′latex−bold′>(A)</span>576<spanclass=′latex−bold′>(B)</span>648<spanclass=′latex−bold′>(C)</span>972<spanclass=′latex−bold′>(D)</span>1152<spanclass=′latex−bold′>(E)</span>1620<span class='latex-bold'>(A) </span>576\qquad<span class='latex-bold'>(B) </span>648\qquad<span class='latex-bold'>(C) </span>972\qquad<span class='latex-bold'>(D) </span>1152\qquad<span class='latex-bold'>(E) </span>1620
2022 A Individual
2022 B Individual #19

Source:

4/30/2022
Cozi makes a two-way table on chalkboard describing the right or left hand usage of students and teachers in her school. However, when she returns to the chalkboard from lunch, she is dismayed to find that most of the numbers on her table have been erased, leaving behind: \begin{tabular}{c c c c} 5 & ? & ? & Total \\ ? & ? & 6 & Total \\ ? & 11 & ? & \\ Total & Total & & \\ \end{tabular} Fortunately, Cozi remembers that the difference between two of the missing numbers is equal to 12.12. Which of the following could be the total number of students and teachers on the table? <spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>15<spanclass=′latex−bold′>(C)</span>16<spanclass=′latex−bold′>(D)</span>17<spanclass=′latex−bold′>(E)</span>18<span class='latex-bold'>(A) </span>14\qquad<span class='latex-bold'>(B) </span>15\qquad<span class='latex-bold'>(C) </span>16\qquad<span class='latex-bold'>(D) </span>17\qquad<span class='latex-bold'>(E) </span>18
2022 B Individual