14. A box of fruit contained twice as many apples as pears. Chris and Lily divided them up so that Chris had twice as many pieces of fruit as Lily. Which one of the following statements is always true?
A Chris took at least one pear.
B Chris took twice as many apples as pears
C Chris took twice as many apples as Lily.
D Chris took as many apples as Lily took pears.
E Chris took as many pears as Lily took apples.
SolUtion
E

Let the total number of pieces of fruit in the box be $3 x$. Since Chris took twice as many pieces of fruit as Lily, he took $2 x$ pieces in total and Lily took $x$ pieces in total. Also, since the box contained twice as many apples as pears, there were $2 x$ apples and $x$ pears in total. Let the number of pears Chris took be $y$. Therefore, since he took $2 x$ pieces of fruit in total, Chris took $2 x-y$ apples, leaving $y$ apples for Lily. Hence the number of apples Lily took is always the same as the number of pears Chris took.

Note: although the argument above shows that option $E$ is always true, it does not show that the others are not. Consider the case where the box contains 2 apples and 1 pear. Chris's options are to take 2 apples, leaving Lily with 1 pear or to take 1 apple and 1 pear, leaving Lily with 1 apple. In the first instance, options $A, B, C$ and $D$ are all untrue and hence none of these can always be true.