We are looking for the only answer choice that CANNOT be true.
(B) states that "more receive $1,000 bonuses than receive $3,000 bonuses."
Let's try to create a scenario in which (B) is true.
First, we'll try to maximize the number of $1k bonuses we assign. - Rule 1 tells us that nobody in the Graphics department can be assigned $1k, which only leaves K, L, M, P as options for recipients of $1k. - However, Rule 3 tells us that L and M are rated Highly Effective, and Rule 2 tells us that this means they receive a larger bonus than the other employees in their department do. So, L and M cannot receive $1k bonuses because they must receive than K and P do. This leaves only K and P as options for recipients of $1k. - Therefore, we can assign $1k bonuses to a maximum of 2 people.
Now, we'll try to minimize the number of $3k bonuses we assign. - Based off Rule 1, the lowest that we can assign to V, X, and Z is $3k. - However, Rule 2 tells us that Highly Effective employees receive a larger bonus than the other employees in their department, and Rule 3 tells us that X was rated Highly Effective. This means that X must be assigned $5k, while V and Z are assigned $3k. - Therefore, we must assign $3k bonuses to a minimum of 2 people.
Our final scenario is as follows: K: 1 L: (3/5) M: (3/5) P: 1 V: 3 X: 5 Z: 3
This scenario shows that we can only have 2 bonuses of $1k, while we can have anywhere from 2 - 4 bonuses of $3k. So, there will always be at least as many $3k bonuses as there are $1k bonuses. Therefore, it is impossible to assign a greater number of $1k bonuses than of $3k bonuses, making (B) the only answer choice that CANNOT be true.
Does that make sense? Please let us know if you have any other questions!
