In a survey of 1,200 shoppers, 72% carried a debit card and 46% carried a credit card, while 30% carried both. What per cent of the shoppers carried neither?

Shoppers carrying at least one card = 72 + 46 - 30 = 88%, because the 30% who carry both were counted in each of the first two figures and must be taken off once. So 100 - 88 = 12% carried neither. 88% is the share who carried at least one - the opposite of what was asked. 18% comes from adding 72 and 46 to get 118% and reading the excess as the answer, which forgets to subtract the overlap. 42% is 72 - 30, those carrying only a debit card.