FROM cars to cucumbers you can always get a bargain if you look around. But do people really understand how they are being manipulated, day-in, day-out when they go shopping?

Psychology plays a big part in sales and marketing. Many people will be familiar with things like placing products in your eyeline or making distinctive brands, so that you know exactly what the product is, so companies even try to clone the look of expensive brands. But the tricks used to persuade us to buy things can also be very subtle.

Shopping can be a mathematical nightmare. There are two for one deals, often called BOGOFs, “buy one get one free”, multi-buy schemes, comparisons between different packs and quantities. It’s a maths jungle out there. Everything these days seems to be on offer.

One of the cleverest ploys is known technically as the “asymmetric dominance effect”, put more simply it’s called the decoy effect. A customer is provided with three choices, but one of them is a choice that few if any customers select (the decoy). The job of the decoy is to make you pick a particular product, the one the company really wants to sell you, while making you feel that you got the best deal, a bargain, even if it isn’t.

I was reminded of this while making my way through the labyrinthine “world of duty free” in Gatwick Airport last week.

There was hardly a product to be seen that didn’t have some associated deal from aftershave to expensive digital cameras. You were faced with signs everywhere indicating sales, bargains and, of course, price comparisons by the lorry load. Navigating and calculating the actual costs, gains, savings and so forth was almost impossible.

There are laws that mean comparisons must be like for like, but this doesn’t mean you can always compare the actual product with its high street equivalent.

Sometimes the comparison is done gram by gram, sometimes it’s fixed quantities like 100ml, but if the product is only 60ml or 80ml, you’re left to do some mental arithmetic. Generally, this doesn’t bother me, my mental arithmetic is OK, but early in the morning or after a long flight even I struggle with simple maths.

So how does the “decoy effect” work? It’s very simple. Imagine you’re looking for a magazine subscription. A print only subscription will cost you £60 and an online only subscription costs £95. Statistically, most people would go for the cheaper print option. But if you were provided with a third option; to get the online and print subscription for £100, statistically more people would opt for that than the print only option. I mean, you’d be mad not to do it wouldn’t you? Two for nearly the price of one.

Of course, the “online only” subscription is the decoy. It focuses your attention on the third option, the one they want you to take. It provides a compelling reason for taking it... you get both.

Suddenly the print only option doesn’t seem to be such a good option now.

The decoy effect can be used on almost anything. Why, for example, do you often choose the “large” popcorn tub at the cinema? Usually because it’s priced just above the medium one and offers nearly twice as much – it’s the one they want you to buy.

That doesn’t make the medium sized one the best offer, as a decoy it is priced so that it looks, and is, expensive.

Maths in marketing can also be deceptive when it comes to ordering food. The next time you order pizza for a group of people think carefully about what you order.

One large pizza is nearly always better than ordering two medium pizzas. This is where GCSE maths can come in handy. Remember all those lessons devoted to working out the area of a circle? It can help you work out which pizza is best value. If you’re offered two 12-inch pizzas or one 18-inch pizza which would you take? Most people go for the 12-inch pizzas, but mathematically you get more pizza if you order the 18-inch one.

Remember your GCSE maths? The formula to calculate the area of a circle is πr2 where r is the radius of the circle (half the diameter). Two 12-inch pizzas give you an area of 226.2 in2, but one 18-inch pizza has an area of 254.5 in2. Of course, you must also think about the crust (not its depth, but its width) and generally the 12-inch pizzas have less non-crust base for toppings. So, provided you can order a half and half pizza to suit different tastes, large is the way to go. At last, your GCSE maths is giving you something useful.