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A box contains 10 tablets of medicine A and 15 tablets

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A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post Updated on: 17 Sep 2014, 05:12
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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.

A. 12
B. 15
C. 17
D. 19
E. 21
Spoiler: OA

Originally posted by schittuluri on 11 Aug 2013, 11:05.
Last edited by Bunuel on 17 Sep 2014, 05:12, edited 2 times in total.
Added the OA.
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 11 Aug 2013, 11:11
2
schittuluri wrote:
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.

A)12
B)15
C)17
D)19
E)21


The worst case scenario will be if we remove all 15 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 15+2=17 tablets.

Answer: C.
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 11 Aug 2013, 13:24
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schittuluri wrote:
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.

A)12
B)15
C)17
D)19
E)21

if we extract 12 then it can be all B, but if 17 then 2kinds of each must have to be there like 15B+2A.....
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 11 Aug 2013, 16:24
I didnt understand ...
if there should be two from each box , the total number shoukdnt be EVEN??

Posted from my mobile device
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 12 Aug 2013, 14:55
2
schittuluri wrote:
I didnt understand ...
if there should be two from each box , the total number shoukdnt be EVEN??

Posted from my mobile device


At least two means 2,3,4,5 etc, so not just even.

12 tablets = 12 B but no A
17 tablets = 15 B and 2 A (even if 15 B extracted)

pick 12 tablets out of the box, chances are that all the 12 tablets are B.
so we have 12 B tablets, not at least two of each kind.

but if we pick 17 tablets out of the box, then even after 15 B we can still have 2 tablets of A.

i mean pick 17 then you have to pick at least 2 from A as well as at least 2 from B.
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 13 Sep 2014, 02:35
why cant we take all of 10 A and then next 2 will be B tablets so total will be 12 and it is the least to ensure we have at least 2 of each type?
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 13 Sep 2014, 06:27
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2
rcformba wrote:
why cant we take all of 10 A and then next 2 will be B tablets so total will be 12 and it is the least to ensure we have at least 2 of each type?


Extracting 12 tablets does not guarantee having at least 2 of each type, because all 12 could be medicine B. In such problems you have to consider the worst case scenario.

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Hope it helps.
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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New post 04 Apr 2017, 15:05
schittuluri wrote:
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.

A. 12
B. 15
C. 17
D. 19
E. 21


Let’s consider the worst possible scenario: It’s possible to take out 15 tablets and all of them are medicine B. In this case, we only take out one kind of medicine instead of both. Therefore, we need to take out at least 15 + 2 = 17 tablets (all 15 of medicine B and 2 of medicine A) to ensure that at least two tablets of each kind are extracted.

Answer: C
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Re: A box contains 10 tablets of medicine A and 15 tablets  [#permalink]

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Re: A box contains 10 tablets of medicine A and 15 tablets   [#permalink] 20 Oct 2019, 13:26
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