It is a cognitive bias known as anchoring bias. In an extremely cited article (according to google it has over 20 thousand cites), cognitive scientists Tversky and Kahneman explain that:
In many situations, people make estimates by starting from an initial value that is adjusted to yield the final answer. The initial value, or starting point, may be suggested by the formulation of the problem, or it may be the result of a partial computation. In either case, adjustments are typically insufficient
and they furthermore propose the following example:
In a demonstration of the anchoring effect, subjects were asked to estimate various quantities, stated in percentages (for example, the percentage of African countries in the United Nations). For each quantity,a number between 0 and 100 was determined by spinning a wheel of fortune in the subjects' presence. The subjects were instructed to indicate first whether that number was higher or lower than the value of the quantity, and then to estimate the value of the quantity by moving upward or downward from the given number. Different groups were given different numbers for each quantity, and these arbitrary numbers had a marked effect on estimates. For example, the median estimates of the percentage of African countries in the United Nations were 25 and 45 for groups that received 10 and 65, respectively, as starting points. Payoffs for accuracy did not reduce not reduce the anchoring effect.
—Judgment under Uncertainty: Heuristics and Biases by Tversky, et al. Science 27 September 1974: 1124-1131. DOI:10.1126/science.185.4157.1124
It is widely used in marketing and advertisement.
For example it is forbidden by law to use this trick to advertise seasonal sales — for example, if a shop sells a pair of shoes for 50£ in January, it cannot expose a "70£ 50£" sign to make it appear as a bargain in February.