Problem:
Six bags of marbles contain , , , , and marbles, respectively. One bag contains chipped marbles only. The other bags contain no chipped marbles. Jane takes three of the bags and George takes two of the others. Only the bag of chipped marbles remains. If Jane gets twice as many marbles as George, how many chipped marbles are there?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Jane gets twice as many marbles as George, so the total number of marbles taken must be divisible by ; that is, the difference between and the number of chipped marbles must be divisible by . Of the six given numbers only has this property. Therefore, there are chipped marbles, leaving for Jane and for George.