You are careful with your money: you collect all kinds of coupons; look for group-buy deals if you eat out; you don't buy clothes unless in a sale. Does all this make you a wise consumer? Let's do the math first: you walk into a coffee shop and see two deals for a cup of coffee. The first deal offers 33 percent extra coffee. The second takes 33 percent off the  regular price. What's the better deal? Well, they are about the same, you'd think. And you'd be wrong. The deals appear to be equal, but in fact, they are different. Here's the math: Let's say the standard coffee is 10 yuan and let's divide the amount of coffee into three portions . That makes about 3.3 yuan per portion, The first deal gets you 4 portions for 10 yuan (2.5 yuan per portion) and the second gets you 3 portions of coffee for 6.6 yuan (2.2 yuan per portion) and is therefore a better deal. In a new study published by the Journal of Marketing, participants were asked the same question, and most of them chose the first deal, the Atlantic website reported. Why? Because getting something extra for free feels better than getting the same for less. The applications of this view into consumer psychology  are huge. Instead of offering direct discounts, shops offer larger sizes or free samples. According to the study, the reason why these marketing tricks work is that consumers don't really know how much anything should cost, so we rely on parts of our brains that  aren't strictly quantitative. There are some traps we should be aware of when shopping. First of all, we are heavily influenced by the first number. Suppose you are shopping in Hong Kong. You walk into Hermes, and you see a 100,000 yuan bag. "That's crazy." You shake your head and leave. The next shop is Gucci, a handbag here costs 25,000 yuan. The price is still high, but compared to the 100,000 yuan price tag you just committed to your memory, this is a steal. Stores often use the price difference to set consumers' expectation. zxxk Another trap we often fall to Is that we are not really sure what things are worth. And so we use clues  to tell us what we ought to pay for them. US economist Dan Ariely has done an experiment to prove this. According to the Atlantic, Ariely pretended he was giving a lecture on poetry. He told one group of students that the tickets cost money and another group that they would be paid to attend. Then he informed both groups that thelecture was free. The first group was anxious to attend, believing they were getting something of value for free. The second group mostly declined, believing they were being forced to volunteer for the same event without reward. What's a lecture on poetry by an economist worth? The students had no idea. That's  the point. Do we really know what a shirt is worth ? What about a cup of coffee? What's the worth of a life insurance.policy? Who knows? Most of us don't. As a result, our shopping  brain uses only what is knowable:  visual  clues, invited emotions, comparisons, and  a sense of bargain. We are not stupid. We are just easily influenced. According to the passage, shops use the following tricks to make more profits EXCEPT  _
showing price differences offering larger sizes providing free samples giving direct discounts