I was practicing my problem-solving and was a bit confused as to why I supposedly got a wrong answer. Below is what I was solving:
Two families are planning to go on a canoe trip together. The families consist of the following people: Robert and Mary Henderson and their three sons Tommy, Dan, and William; Jerome and Ellen Penick and their two daughters Kate and Susan. There will be three canoes, with three people in each canoe. At least one of the four parents must be in each canoe. At least one person from each family must be in each canoe. Question: If each of the Henderson children ride in a different canoe, which of the following must be true? (I) The Penick children do not ride together (II) The Penick parents do not ride together (III) The Henderson parents do not ride together
a) I only
b) II only
c) I and II only
d) I and III only
My answer is d) but apparently the correct answer might be a).
So let's assume that III is false (that the Henderson parents do ride together).
Then the statements "at least one person from each family must be in each canoe" and "each of the Henderson children ride in a different canoe" cannot both be followed since there are 3 canoes and 3 Henderson children. But if a Henderson child rides in the same canoe containing both Henderson parents, then it is full and does not contain a member of the other family.
Can anyone confirm if I'm right or wrong? Thanks.
To solve this problem, we can use a method called "elimination" to determine which statements must be true.
Let's start by assuming that statement (III) is false, meaning that the Henderson parents ride together. In this case, we know there are three canoes, and at least one parent from each family must be in each canoe. Since the Henderson parents ride together, one of them must be in a canoe with Penick parents, and the other Henderson parent must be in a separate canoe with at least one Penick parent.
Now, let's consider whether the other conditions can be satisfied with this arrangement. We know that each of the Henderson children must ride in a different canoe. With the Henderson parents riding together, this means that there are only two canoes left for the remaining three Henderson children. So, it is not possible to have each of the Henderson children ride in a different canoe if the Henderson parents ride together.
Since we have found a contradiction, we can conclude that statement (III) must be true. Therefore, we can eliminate options a) and b) since they do not include statement (III).
Now, let's consider whether statement (I) is true or false. If the Penick children ride together, then there would be two Penick children in one canoe and one Penick child in another canoe. Since there must be at least one parent from each family in each canoe, this would mean that one of the Penick parents would have to be with two of their children and the other parent with only one child, which violates the condition.
Therefore, we can conclude that statement (I) must be true. This leads us to the correct answer, which is option a) I only.
In summary, using the method of elimination, we can determine that statement (III) must be true, and statement (I) must also be true. This means that the correct answer is option a) I only.