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M07-35

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M07-35  [#permalink]

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New post 16 Sep 2014, 00:36
2
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:00) correct 44% (01:08) wrong based on 73 sessions

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There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3
Spoiler: OA

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Re M07-35  [#permalink]

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New post 16 Sep 2014, 00:36
1
2
Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

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: M07-35  [#permalink]

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New post 14 Nov 2015, 05:54
imagine we pick any chip first and put it on the table - no matter what color. next we drag the second and put it next to the first. if we are lucky these 2 chips will be either black or white (less probable) but if not we need to pick another one because we have a combination of black and white:

BL WH

So what happens next? We drag out whatever chip it is and place it on the table - voila we guarantee we will have a pair: either a pair of 2 blacks or a pair of 2 whites
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Re: M07-35  [#permalink]

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New post 02 Jan 2016, 11:20
That's a simple one. If we take three , at least two will be of same type. Hence, answer is 3.
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Re: M07-35  [#permalink]

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New post 24 Jul 2016, 18:51
Bunuel wrote:
Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: E





hello!
please help me in understanding two concepts:
1) what if he picks 7... hence covering minimum of two of same color
2) what if he picks up 17.. hence covering minimum of two of same color?
thanks
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Re: M07-35  [#permalink]

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New post 24 Jul 2016, 22:02
Celestial09 wrote:
Bunuel wrote:
Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: E





hello!
please help me in understanding two concepts:
1) what if he picks 7... hence covering minimum of two of same color
2) what if he picks up 17.. hence covering minimum of two of same color?
thanks


I don't understand what you mean there...

Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
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Collection of Questions:
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Re: M07-35  [#permalink]

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New post 01 Apr 2017, 13:25
shouldnt the least amount of chips needed to be picked be 5? this is because after we remove 5 black chips, we will only have white chips making it sure that any two chips are of same colour. Bunuel I was unable to understand your explanation; please elaborate. Thanks.
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New post 02 Apr 2017, 05:19
OreoShake wrote:
shouldnt the least amount of chips needed to be picked be 5? this is because after we remove 5 black chips, we will only have white chips making it sure that any two chips are of same colour. Bunuel I was unable to understand your explanation; please elaborate. Thanks.


What is the least number of chips we should pick to guarantee that we have 2 chips of the same color? So, we need to have tow white or two black chips.

The worst case would be if for the first two pick we'll get one black and one white chips: BW or WB. The next (3rd) chip will be B or W in any case we'll have two chips of the same color: BW - W or BW - B.

You should check other worst case scenario questions. Link is in the post above.
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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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New post 02 Apr 2017, 05:58
Bunuel wrote:
OreoShake wrote:
shouldnt the least amount of chips needed to be picked be 5? this is because after we remove 5 black chips, we will only have white chips making it sure that any two chips are of same colour. Bunuel I was unable to understand your explanation; please elaborate. Thanks.


What is the least number of chips we should pick to guarantee that we have 2 chips of the same color? So, we need to have tow white or two black chips.

The worst case would be if for the first two pick we'll get one black and one white chips: BW or WB. The next (3rd) chip will be B or W in any case we'll have two chips of the same color: BW - W or BW - B.

You should check other worst case scenario questions. Link is in the post above.


Hmm, I guess i understood the question incorrectly; i had inferred how many picks till we guarantee two colors same in a ROW. Thanks Bunuel.
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M07-35  [#permalink]

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New post 21 Feb 2019, 07:11
Bunuel wrote:
Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: E


Hi Bunuel

Please help me understand this.

IMO,

For a best scenario(Least no of picks) We should select minimum 6 to ensure that one color chips are exhausted.
For a worst scenario(Max no of picks) we should select minimum 17 to ensure the same.

If we are picking 2, then why are we considering the third to be of the other color ? why not of the same color as we have picked before ?

Please help me evaluate my thought process.
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Re: M07-35  [#permalink]

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New post 21 Feb 2019, 07:35
Manas1212 wrote:
Bunuel wrote:
Official Solution:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?

A. 19
B. 16
C. 6
D. 5
E. 3

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: E


Hi Bunuel

Please help me understand this.

IMO,

For a best scenario(Least no of picks) We should select minimum 6 to ensure that one color chips are exhausted.
For a worst scenario(Max no of picks) we should select minimum 17 to ensure the same.

If we are picking 2, then why are we considering the third to be of the other color ? why not of the same color as we have picked before ?

Please help me evaluate my thought process.


I think you misunderstood the question. The question asks about the number of picks to guarantee that we have either two black or two white chips.

The worst case would be if we pick one black and one white for the first two picks. The next one will be either black or white. So, after three picks we for sure will have at least two black or at least two white chips.

Does this make sense?

Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
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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.


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Re: M07-35  [#permalink]

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New post 22 Feb 2019, 05:12
Hi

Can someone explain how this question is different from the one below:

A box contains 10 tablets of medicine A and 15 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted?
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Re: M07-35   [#permalink] 22 Feb 2019, 05:12
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