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Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol settles all the debts by giving money to both Anne and Bob, how much will she give Anne?

Re: Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol [#permalink]

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05 Oct 2017, 05:52

1

This post received KUDOS

Anne has to give $4 to someone and receive $5 from someone. So in all, she has to receive $1 Bob has to give $3 to someone and receive $4 from someone. So in all, he has to receive $1 Carol has to give $5 to someone, and receive $3 from someone. So in all, she has to give $2

So in summary, A and B have to receive $1 each while C has to give $2. This entire thing can be settled if C gives $1 each to A as well as B.

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol [#permalink]

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05 Oct 2017, 17:34

Bunuel wrote:

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol settles all the debts by giving money to both Anne and Bob, how much will she give Anne?

A. $1 B. $2 C. $3 D. $4 E. $5

I made a small table of what each person owed (-x) or was owed (+x), summed, and got a result that pointed me to what I think is the answer.

That said, this question is WEIRD. I gave it kudos. Maybe if I were a CPA or CFO I would not be bug-eyed at the average of 30 seconds to solve correctly. . .

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol settles all the debts by giving money to both Anne and Bob, how much will she give Anne?

A. $1 B. $2 C. $3 D. $4 E. $5

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.

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol settles all the debts by giving money to both Anne and Bob, how much will she give Anne?

A. $1 B. $2 C. $3 D. $4 E. $5

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$.

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol [#permalink]

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06 Oct 2017, 06:20

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.
_________________

At the still point, there the dance is. -- T.S. Eliot Formerly genxer123

Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol settles all the debts by giving money to both Anne and Bob, how much will she give Anne?

A. $1 B. $2 C. $3 D. $4 E. $5

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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