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M21-24

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M21-24 [#permalink]

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If a box contains 10 red pills, 5 blue pills, and 12 yellow pills, what is the least number of pills one must extract from the box to ensure that at least three pills of each color are among those extracted?

A. 12
B. 17
C. 18
D. 23
E. 25
[Reveal] Spoiler: OA

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Re M21-24 [#permalink]

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New post 16 Sep 2014, 01:11
Official Solution:

If a box contains 10 red pills, 5 blue pills, and 12 yellow pills, what is the least number of pills one must extract from the box to ensure that at least three pills of each color are among those extracted?

A. 12
B. 17
C. 18
D. 23
E. 25

In the worst possible scenario, one will draw 22 pills without drawing a single blue pill. To make sure that there will be 3 blue pills among the extracted, one has to draw 3 more than 22 (i.e. 25).

Answer: E
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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

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Re: M21-24 [#permalink]

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New post 01 Jul 2015, 06:13
Hi,

I think the anser is pretty logic, simple and fast. But I have one doubt... what if I have to solve with combinatorics formulas "C", wich would be the right solution?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700

Kudos [?]: 2 [0], given: 22

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Re: M21-24 [#permalink]

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New post 01 Jul 2015, 06:19
luisnavarro wrote:
Hi,

I think the anser is pretty logic, simple and fast. But I have one doubt... what if I have to solve with combinatorics formulas "C", wich would be the right solution?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700


This is not combinations question, it's a so called worst case scenario, min/max, question.

Check other Worst Case Scenario Questions from our Special Questions Directory to practice.

Hope it helps.
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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.


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Re: M21-24 [#permalink]

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New post 01 Jul 2015, 07:36
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Bunuel wrote:
luisnavarro wrote:
Hi,

I think the anser is pretty logic, simple and fast. But I have one doubt... what if I have to solve with combinatorics formulas "C", wich would be the right solution?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700


This is not combinations question, it's a so called worst case scenario, min/max, question.

Check other Worst Case Scenario Questions from our Special Questions Directory to practice.

Hope it helps.


Thanks a lot¡¡¡

Regards.

Luis Navarro Looking for 700

Kudos [?]: 2 [1], given: 22

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Joined: 02 Sep 2009
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Re: M21-24 [#permalink]

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New post 01 Jul 2015, 07:38
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Expert's post
luisnavarro wrote:
Bunuel wrote:
luisnavarro wrote:
Hi,

I think the anser is pretty logic, simple and fast. But I have one doubt... what if I have to solve with combinatorics formulas "C", wich would be the right solution?

Thanks a lot.

Regards.

Luis Navarro
Looking for 700


This is not combinations question, it's a so called worst case scenario, min/max, question.

Check other Worst Case Scenario Questions from our Special Questions Directory to practice.

Hope it helps.


Thanks a lot¡¡¡

Regards.

Luis Navarro Looking for 700


Please use KUDOS button instead of "thank you" messages. Thank you!
_________________

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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Kudos [?]: 128443 [1], given: 12173

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Re: M21-24 [#permalink]

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New post 12 Sep 2017, 08:05
Hi Bunuel,

The question has asked for the least number of balls that can be extracted.

For that reason I chose 18 as an answer. Can you please explain the solution in detail and why 18 isn't right.
15 balls (without any yellow balls), then 3 more to include at least 3 yellow and that makes the total as 18.

Please correct me what is wrong with my logic.

Thanks!

Kudos [?]: [0], given: 182

Expert Post
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Joined: 02 Sep 2009
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Re: M21-24 [#permalink]

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New post 12 Sep 2017, 08:10
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shalini14 wrote:
Hi Bunuel,

The question has asked for the least number of balls that can be extracted.

For that reason I chose 18 as an answer. Can you please explain the solution in detail and why 18 isn't right.
15 balls (without any yellow balls), then 3 more to include at least 3 yellow and that makes the total as 18.

Please correct me what is wrong with my logic.

Thanks!


We want to ensure that at least three pills of each color are among those extracted. 18 is not correct answer because we can have 10 red pills and then 8 yellow pills and we still won't have three pills of 3 different colors.

For more check other Worst Case Scenario Questions from our Special Questions Directory to practice.

Hope it helps.
_________________

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 [?]: 128443 [0], given: 12173

Re: M21-24   [#permalink] 12 Sep 2017, 08:10
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