A. weak B. as C. difficult D. convincing E. missing F. surprise G. consumption H. prices I. conversely J. help K. foxed L. off M. overwhelmingly N. spot O. dumb When shopkeepers want to lure customers into buying a particular product, they typically offer it at a discount .According to a new study to be published in the Journal of Marketing ,they are(1) a trick . A team of researchers ,led by Akshay Rao of University of Minnesota, looked at consumers' attitudes to discounting .Shoppers, they found,much prefer getting something extra free to getting cheaper .The main reason is that most people are ( 2) at fractions . Consumers often struggle to realise ,for example ,that a 50% increase in quantity is the same as a 33% discount in price. They(3) assume the former is better value .In an experiment, the researchers sold 73% more hand lotion when it was offered in a bonus pack than when it carried an equivalent discount . This numerical blind (4) remains even when the deal clearly favours the discounted product .In another experiment ,this time on his undergraduates, Mr .Rao offered two deals on loose coffee beans:33% extra free or 33% (5) the price .The discount is by far the better proposition ,but the experiment shows the supposedly clever students viewed them ( 6) equivalent. Marketing types can draw lessons beyond just pricing ,says Mr. Rao. When advertising a new car's efficiency ,for example ,it is more (7) to talk about the number of extra miles per gallon it does ,rather than the equivalent percentage fall in fuel ( 8) . There may be lessons for officials who regulate prices too .Even well-educated shoppers are easily (9) . Sending everyone back to school for maths seems out of the question .But more prominently displayed unit prices in shops and advertisements would be a great(10)________.