MathDB

25

Part of 2019 MIG

Problems(1)

2019 Individual #25

Source:

5/1/2022
Each day John's mother sends him to the store with $1\$1 to buy widgets and gadgets, each of which cost a whole number of cents. On the first day John comes back with 44 widgets, 55 gadgets, and 3535 cents in change. On the second day, John comes back with 55 widgets, 44 gadgets, and 3939 cents in change. On the third day, John comes back with only cc cents in change. He hands his mother the change, telling her that he had tripped coming home and broken all the widgets and gadgets. His mother, thinking for a moment, begins yelling at him for lying, as she noticed that there was no way he could have received exactly cc cents in change given the price of widgets and gadgets. What is the sum of the digits of the least possible value of cc?
<spanclass=latexbold>(A)</span>10<spanclass=latexbold>(B)</span>13<spanclass=latexbold>(C)</span>15<spanclass=latexbold>(D)</span>18<spanclass=latexbold>(E)</span>impossible to determine<span class='latex-bold'>(A) </span>10\qquad<span class='latex-bold'>(B) </span>13\qquad<span class='latex-bold'>(C) </span>15\qquad<span class='latex-bold'>(D) </span>18\qquad<span class='latex-bold'>(E) </span>\text{impossible to determine}
2019 Individual