When retailers want to entice customers to buy 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 missing a 1. A team of researchers, led by Akshay Rao of the University of Minnesota's Carlson School of Management, looked at consumers' attitudes to discounting. Shoppers, they found, much prefer getting something extra free to getting something cheaper. The main reason is that most people are 2at fractions. Consumers often 3to realise, for example, that a 50% increase in quantity is the same as a 33% discount in price. They overwhelmingly assume the former is better value. In an experiment, the researchers sold 73% more hand lotion when it was 4 in a bonus pack than when it carried an equivalent discount. This numerical blind spot remains even when the deal clearly favor 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% off the price. The discount is by far the better proposition, but the 5clever students viewed them as equivalent. Studies have shown other ways in which retailers can exploit consumers' innumeracy. One is to confuse them with double discounting. People are more likely to see a 6in a product that has been reduced by 20% , and then by an additional 25% , than one which has been bargain to an equivalent, one-off, 40% 7. Marketing types can draw lessons beyond just pricing, says Mr. Rao. When advertising a new car's 8, for example, it is more 9 to talk about the number of extra miles per gallon it does, rather than the equivalent percentage fall in fuel 10 .A) bargain I) paidB) consumption J) persuadingC) convincing K) reductionD) deduction L) straggleE) doubtfully M) supposedlyF) efficiency N) trickG) hopeless O) uselessH) afforded