A research group conducted a survey of 500 consumers and reported that 370 consumers preferred product \(X\) and 240 consumers preferred product \(Y\). What is the least number that must have preferred both the products?
110
By the inclusion-exclusion principle, the number preferring both products is at least \(|X|+|Y|-\text{total}=370+240-500=110\). So the least number who must have preferred both products is 110.
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