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

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

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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?

A. $1
B. $2
C. $3
D. $4
E. $5
[Reveal] Spoiler: OA

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

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New post 05 Oct 2017, 06:52
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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.

So she will give $1 to Anne. A answer

Kudos [?]: 130 [1], given: 260

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Kudos [?]: 258 [0], given: 547

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

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New post 05 Oct 2017, 18:34
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. . .

__B__|__A__|__C__|
_+4__|_-4__|_-5__|
_-3__|_+5__|_+3__|
--------------------------
_+1__|_+1__|_-2__|RESULT

I decided that those numbers mean: Carol owes $2.
Carol gives both Bob and Ann the $1 each of them is owed.

Carol gives Ann $1.

Answer C

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

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New post 06 Oct 2017, 00:59
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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


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)
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Kudos [?]: 17349 [1], given: 232

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

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New post 06 Oct 2017, 01:12
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Expert's post
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


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128752 [1], given: 12182

Director
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Joined: 22 May 2016
Posts: 807

Kudos [?]: 258 [0], given: 547

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

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New post 06 Oct 2017, 07:20
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.

Kudos [?]: 258 [0], given: 547

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

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New post 09 Oct 2017, 16:41
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


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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Re: Anne owes Bob $4, Bob owes Carol $3, and Carol owes Anne $5. If Carol   [#permalink] 09 Oct 2017, 16:41
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