Question

Cathy has less money than David. Cathy and David together have as much money as Alice and Bob together. Alice and David together have less money than Bob and Cathy together. What is the correct richest-poorest pairing?

• A. Bob-Cathy
• B. Bob-Alice
• C. David-Cathy
• D. Cathy-Alice

Answer 1

The Correct Option is B

To solve this problem, we need to analyze the relationships given in the statements. Let's denote the amount of money each person has as follows: Cathy = C, David = D, Alice = A, and Bob = B. We'll extract information from the statements and use inequalities to compare:

1. Cathy has less money than David: \(C < D\)

2. Cathy and David together have as much money as Alice and Bob together: \(C + D = A + B\)

3. Alice and David together have less money than Bob and Cathy together: \(A + D < B + C\)

Our goal is to identify the richest-poorest pairing from the options:

Option	Richest-Poorest Pair
1	Bob-Cathy
2	Bob-Alice
3	David-Cathy
4	Cathy-Alice

We will use the information to deduce the richest and poorest individuals:

1. From \(C < D\), Cathy is poorer than David.
2. If we express \(C + D = A + B\), this suggests that the total amounts are equal, but individual amounts aren’t necessarily equal.
3. Using \(A + D < B + C\), since Cathy is known to be the poorest from \(C < D\), the inequality reinforces the idea that Bob is likely to compensate and be the richest among them.

This analysis shows that Bob is likely the richest, and Alice is balanced, leaving Cathy as the poorest. Therefore, the correct richest-poorest pairing based on given options is:

Bob-Alice