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If a librarian randomly removes science books from a library

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If a librarian randomly removes science books from a library  [#permalink]

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New post 08 May 2010, 09:54
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If a librarian randomly removes science books from a library of which 50 are on botany, 65 on zoology, 90 on physics, 50 on geology and 110 on chemistry then how many books must be removed to ensure that 80 of the removed books are on the same science.?
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 08 May 2010, 15:10
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bibha wrote:
1. If a librarian randomly removes science books from a library of which 50 are on botany, 65 on zoology, 90 on physics,50 on geology and 110 on chemistry then how many books must be removed to ensure that 80 of the removed books are on the same science.?

:-)
Solution pleaseeeeeeeeeeeeeee


We can pick 80 books only from physics or from chemistry. Worst case scenario would be if we pick all books from botany, zoology, geology, 79 books from physics and 79 books from chemistry.

We would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either in physics or chemistry.

Answer 323+1=324.

Check the following links for the similar problems:
probability-question-85216.html#p638310
least-of-cards-83183.html#p623657
why-the-worst-case-scenario-86217.html#p647722
at-least-combinatorics-pills-56779.html#p668774
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 08 May 2010, 14:56
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bibha wrote:
1. If a librarian randomly removes science books from a library of which 50 are on botany, 65 on zoology, 90 on physics,50 on geology and 110 on chemistry then how many books must be removed to ensure that 80 of the removed books are on the same science.?

:-)
Solution pleaseeeeeeeeeeeeeee


Catch here is to find the no. of book to "ENSURE" that we get get 80 books of any one subject.. and we can see that that subject cannot be bota, zoo and Geo..

So let say we start removing the books in a such a manner that we "delay" the process to remove 80 book of one subject.....How we can do that...??

Bota 50
Zoo 65
Phy 90
Geo 50
Chem 110

Pick 50 books of each subject...and we see that we have picked 50*5=250 books without actually picking 80 books of one particular subject... Now we are left with following stats..

Bota 00
Zoo 15
Phy 40
Geo 00
Chem 60

Pick 15 books of each subject...and we see that we have picked 15*3= 45 more books and we are still not done with "picking 80 books of one particular subject"... Now we are left with following stats.. and we have received a maximum of 65 books any subject....!!!

Bota 00
Zoo 00
Phy 25
Geo 00
Chem 45

Pick 14 books of each subject...and we see that we have picked 14*2= 28 more books and we are still not done with "picking 80 books of one particular subject"..Now we are left with following stats.. and we have received a maximum of 79 books any subject....!!!

Bota 00
Zoo 00
Phy 11
Geo 00
Chem 31

So total books picked till now = 250 + 45 + 28.

So if we pick one more book, we are "SURE" that we will have now 80 books..of one subject..!!
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 08 May 2010, 15:05
is it 80 of the books or 80% of the books? question does not seems to be clear.
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 09 May 2010, 02:57
good question ......
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 09 May 2010, 23:11
Hey,
Thanks, I really liked the concept used by Bunuel.
:-)
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Re: Arithmetic,combination,permutation...confused `~~  [#permalink]

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New post 18 May 2010, 16:57
Bunuel wrote:
bibha wrote:
1. If a librarian randomly removes science books from a library of which 50 are on botany, 65 on zoology, 90 on physics,50 on geology and 110 on chemistry then how many books must be removed to ensure that 80 of the removed books are on the same science.?

:-)
Solution pleaseeeeeeeeeeeeeee


We can pick 80 books only from physics or from chemistry. Worst case scenario would be if we pick all books from botany, zoology, geology, 79 books from physics and 79 books from chemistry.

We would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either in physics or chemistry.

Answer 323+1=324.

Check the following links for the similar problems:
probability-question-85216.html#p638310
least-of-cards-83183.html#p623657
why-the-worst-case-scenario-86217.html#p647722
at-least-combinatorics-pills-56779.html#p668774

great concept used !!
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Re: If a librarian randomly removes science books from a library  [#permalink]

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New post 09 Jun 2015, 16:46
Bunuel wrote:
bibha wrote:
1. If a librarian randomly removes science books from a library of which 50 are on botany, 65 on zoology, 90 on physics,50 on geology and 110 on chemistry then how many books must be removed to ensure that 80 of the removed books are on the same science.?

:-)
Solution pleaseeeeeeeeeeeeeee


We can pick 80 books only from physics or from chemistry. Worst case scenario would be if we pick all books from botany, zoology, geology, 79 books from physics and 79 books from chemistry.

We would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either in physics or chemistry.

Answer 323+1=324.

Check the following links for the similar problems:
probability-question-85216.html#p638310
least-of-cards-83183.html#p623657
why-the-worst-case-scenario-86217.html#p647722
at-least-combinatorics-pills-56779.html#p668774


Check other Worst Case Scenario Questions from our Special Questions Directory.
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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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: If a librarian randomly removes science books from a library  [#permalink]

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