A state seed corporation raises its seed on two farms and tests every lot for germination, the first farm passing a higher share of its lots than the second in each of the two seasons. On each farm the share of lots passing was higher last season than in the season before. Yet for the corporation's seed taken as a whole, the share of lots passing was lower last season than in the season before. Which of the following must be true?

The corporation's figure is the two farms' figures weighted by how many lots each contributed, so if both weighted quantities rose and the weighted result fell, the weights must have shifted towards the weaker farm. Take it in numbers: 90 of 100 lots from the first farm passing 90 in every hundred and 10 from the second passing 40 gives 85 overall; next season the first passes 92 and the second 45, but only 20 lots come from the first and 80 from the second, and the whole falls to about 54. The first option contradicts what is given. Fewer lots in all is possible but nowhere forced — the totals may be identical. And which farm improved more is not fixed either; in the illustration the second improved by more.