in a village there are 100 houses. there is a dog in 90 houses, a cat in 80 houses, a rabbit in 75 houses and a turtle in 65 houses. Among those 100 houses, how many, at least, have a dog, a cat, a rabbit, and a turtle?
10
To find the minimum number of houses that have a dog, a cat, a rabbit, and a turtle, we need to determine the highest number of houses that have all four animals present.
We know that the dog is in 90 houses, the cat is in 80 houses, the rabbit is in 75 houses, and the turtle is in 65 houses. We want to find the maximum number of houses that have all four animals, so we look for the smallest overlapping count among these numbers.
If we examine the given numbers, we can see that the maximum number of houses where all four animals are present is determined by the turtle, as it is present in the fewest houses (65 houses). This means that the number of houses that have all four animals is at most 65.
However, we also need to consider the possibility that some houses might have all four animals, even though it is not explicitly mentioned in the given information. In other words, we assume that the numbers provided for each animal are not mutually exclusive.
Since we have 100 houses in total, and we know the maximum number of houses with all four animals is 65, it means that at least 65 houses have all four animals (as it is possible that there could be more than 65 houses with all four animals).
Therefore, the minimum number of houses that have a dog, a cat, a rabbit, and a turtle is 65.