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A gambler bought $3,000 worth of chips at a casino in

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A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 25 Feb 2012, 22:23
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A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?

$2,040
$2,120
$1,960
$1,920
$1,400

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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 25 Feb 2012, 23:29
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Chembeti wrote:
A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?

A. $2,040
B. $2,120
C. $1,960
D. $1,920
E. $1,400


In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.

So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.

Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $3,000-$880=$2,120.

Answer: B.
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 25 Feb 2012, 23:41
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Bunuel wrote:
Chembeti wrote:
A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?

A. $2,040
B. $2,120
C. $1,960
D. $1,920
E. $1,400


In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost. So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips lost.

Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $3,000-$880=$2,120.

Answer: B.


I somehow got confused with the wordings.... :cry:
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 25 Feb 2012, 23:44
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 25 Feb 2012, 23:59
Bunuel wrote:
Chembeti wrote:
I somehow got confused with the wordings.... :cry:


With the wording of the question or the wording of the solution? Please let me know if anything needs farther clarification.


Your answer is perfect. I got confused with the question. :-D
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 26 Feb 2012, 00:47
Great approach to min/max questions. With @bunuel around, I guess the learning never ends...thanks.
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 26 Feb 2012, 00:53
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fortsill wrote:
Great approach to min/max questions. With @bunuel around, I guess the learning never ends...thanks.


Min/max questions are quite common on the GMAT. Check our question banks for such kind of problems to practice:

DS: search.php?search_id=tag&tag_id=42
PS: search.php?search_id=tag&tag_id=63

Hope it helps.
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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?
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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New post 13 Nov 2016, 10:24
Answer:B
1- Largest amount of money that the gambler could have received back ⇒ the lost amount is minimum ⇒ $100 amount lost is minimum
2- $20 chips lost was 2 more or 2 less than the number of $100 chips lost ⇒ Lost $100 is minimum and $20 is maximum
-1- and -2- ⇒ $20 chips lost is 9 and $100 chips lost is 7 ⇒ total loss=20x9+100x7=$880 ⇒ He received back=3000-880= $2120
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Re: A gambler bought $3,000 worth of chips at a casino in  [#permalink]

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