Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, one in a coffee shop, one in a shopping mall, and one in the library. You know the following.
a.If Kay was not discovered in the library, then Amy was discovered in the apartment building.
b.Beth was discovered in the library, unless Mary was discovered in the coffee shop.
c.If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.
d.If Beth was not discovered in the library, then neither was Kay.
If you have enough information from the statements above, match the girl with the location in which she was discovered and explain your reasoning. If you cannot make the match, explain why.
To solve this problem, we need to carefully analyze each statement and use logical reasoning to deduce the matching of the girls with the locations where they were discovered. Let’s go through each statement one by one:
a. If Kay was not discovered in the library, then Amy was discovered in the apartment building.
From this statement, we can conclude that if Kay is not in the library, then Amy must be in the apartment building.
b. Beth was discovered in the library, unless Mary was discovered in the coffee shop.
This statement tells us that either Beth is in the library, or Mary is in the coffee shop. It gives us two possibilities.
c. If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.
This statement establishes a relationship between Amy being in the apartment building and Mary being in the shopping mall. If Amy is in the apartment building, then Mary must be in the shopping mall.
d. If Beth was not discovered in the library, then neither was Kay.
This statement means that if Beth is not in the library, then Kay cannot be in the library either.
Based on these statements, let’s consider each possibility:
1. Beth is in the library, and Mary is in the coffee shop.
From statement b, if Beth is in the library, it means Mary cannot be in the coffee shop. However, statement c says that if Amy is in the apartment building, then Mary must be in the shopping mall. Therefore, this possibility is not valid.
2. Mary is in the coffee shop, and Beth is not in the library.
If Mary is in the coffee shop, following statement c, it means Amy must be in the apartment building. And if Beth is not in the library (according to statement d), Kay cannot be in the library either. We are left with Kay being in the shopping mall. These fulfill all the conditions, and therefore, this possibility is valid.
So, the matching will be:
- Amy was discovered in the apartment building.
- Mary was discovered in the coffee shop.
- Kay was discovered in the shopping mall.
- Beth was discovered in the library.
Therefore, based on the given statements, we can determine the match between the girl and the location where she was discovered.