Problem:
Ximena lists the whole numbers through once. Emilio copies Ximena's numbers, replacing each occurrence of the digit by the digit . Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximena's sum than Emilio's?
Answer Choices:
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B.
C.
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E.
Solution:
Each time Emilio replaces a in the ones position by , Ximena's sum is decreased by . When Emilio replaces a in the tens position by , Ximena's sum is decreased by . Ximena wrote twos in the ones position and twos in the tens position . Thus Ximena's sum is greater than Emilio's sum by .
The problems on this page are the property of the MAA's American Mathematics Competitions