A state department reports that 40,000 households of the district hold a job card, 26,000 hold a card for the fair price shop and 14,000 are on the housing list, and concludes that 80,000 of the district's households are covered by at least one of the three schemes. Which of the following is an assumption on which the department's conclusion depends?

Forty, twenty-six and fourteen thousand add to eighty thousand only as a count of households if the three lists have nobody in common, and since these are all schemes for households of small means the same family is very likely to be on two of them or on all three. The conclusion therefore rests entirely on the lists not overlapping, and if they overlap heavily the true figure may be barely half the reported one. Which department runs the schemes bears on their administration. Whether a job-card holder has worked bears on the scheme's use rather than on the household's coverage by it. And what a card holder draws from the fair price shop concerns the benefit received, not whether the same household has been counted twice.