Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol

Though, under pressure, the logic can seem twisted, the question gives you a good tip. Carol settles the debts by paying both Anne and Bob. So all in all, Anne and Bob are to receive some money. How much?
Anne owes $4 and has to receive $5. So all in all, she has to get $1. Carol must have paid her this amount to settle her account.

Answer (A)

Shortcut solution:

Anne owes someone 4$ and another person owes her 5$ (so her balance is +1). If all debts are settled not by Anne (as stated), Anne should gain 1$. Answer 1.

Answer: A.

Step by step:

We are told that: "Carol settles all the debts by giving money to both Anne and Bob" --> which means that by this one only action (giving money to both Anne and Bob) Carol settles ALL debts. How this can happen?

The balances of each:

Anne: +1(5-4)
Bob: +1 (4-3)
Carol: -2 (3-5)

So if Carol wants to settle all the debts she must give 1$ to Anne and 1$ to Bob. After this operation by Carol all the debts would be settled. So Carol should give Anne 1$.

Answer: A.

VeritasPrepKarishma and Bunuel , thank you for your posts. I am no longer trying to imagine an unwieldy skein of money exchanges among three people. The question's logic seems less tortured. Your narrowing of focus made strategic sense.

Thanks and kudos for all your help and hard work. Much appreciated.

Let’s assume each person has $10 before they pay off their debts.

Since Anne owes Bob $4 but Carol owes Anne $5, we see that Anne will have a net gain of $1. Thus, Anne will have $11 after her debt settles.

Similarly, Bob will have a net gain of $1, since he owes Carol $3 but Anne owes him $4. Thus, Bob will have $11 after his debt settles.

Finally, Carol will have a net loss of $2, since she owes Anne $5 but Bob only owes her $3. Thus, Carol will have $8 after her debt settles.

Since the problems says Carol settles her debts by giving money to both Anne and Bob, she must give each $1 (since her total loss is $2, and assuming the dollar amounts are whole numbers). So, Carol gives Anne $1.

Answer: A

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