A box contains 10 red pills 5 blue pills 12 yellow : GMAT Problem Solving (PS)
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# A box contains 10 red pills 5 blue pills 12 yellow

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A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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07 Dec 2007, 11:03
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A box contains
10 red pills
5 blue pills
12 yellow pills.

What is the least number of pills one must extract to ensure at least
1. one blue pill?
2. two blue pills?
3. one blue and one yellow?
4. two blue and one yellow?
5. two blue and two yellow?
6. at least one of each color?
7. at least 3 of each color?
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Re: at least - combinatorics - pills [#permalink]

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07 Dec 2007, 12:03
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A box contains
10 red pills
5 blue pills
12 yellow pills.

What is the least number of pills one must extract to ensure at least
1. one blue pill? 10+12+1=23
2. two blue pills? 10+12+2=24
3. one blue and one yellow? 10+12+1=23
4. two blue and one yellow? 10+12+2=24
5. two blue and two yellow? 10+12+2=24
6. at least one of each color? 10+12+1=23
7. at least 3 of each color? 10+12+3=25
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 18:40
walker wrote:
3. one blue and one yellow? 10+12+1=23
4. two blue and one yellow? 10+12+2=24
5. two blue and two yellow? 10+12+2=24
6. at least one of each color? 10+12+1=23
7. at least 3 of each color? 10+12+3=25

On #3 - 7, why do you add 12 yellow instead of 5 blue? The question asks for the least number of pills to insure the combination. So, for example, for #3 - in order to ensure the least possible number of pills AND one blue and one yellow, can we have:

10 Red + 5 Blue + 1 Yellow = 16 total vs. 10Red + 12Yellow + 1Blue = 23 in the answer above

I applied the same approach to #4-7.

Last edited by JuliaS on 20 Jan 2008, 19:09, edited 2 times in total.
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 18:54
Silly question, but arent the least number of pills, at least for question 1, one ? I.e. the first pill you pick is the blue one ??
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 19:13
pmenon wrote:
Silly question, but arent the least number of pills, at least for question 1, one ? I.e. the first pill you pick is the blue one ??

these are worst case scenario problems. we want the max number of wrong pills before we get the correct pills.

we want to pull out the max number of other pills and then the correct pill in order to ENSURE that we get a correct pill.
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 19:16
bmwhype2 wrote:
pmenon wrote:
Silly question, but arent the least number of pills, at least for question 1, one ? I.e. the first pill you pick is the blue one ??

these are worst case scenario problems. we want the max number of wrong pills before we get the correct pills.

we want to pull out the max number of other pills and then the correct pill in order to ENSURE that we get a correct pill.

So what is wrong with my approach on #3 then: 10 Red + 5 Blue + 1 Yellow = 16 ?
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 19:20
JuliaS wrote:
bmwhype2 wrote:
pmenon wrote:
Silly question, but arent the least number of pills, at least for question 1, one ? I.e. the first pill you pick is the blue one ??

these are worst case scenario problems. we want the max number of wrong pills before we get the correct pills.

we want to pull out the max number of other pills and then the correct pill in order to ENSURE that we get a correct pill.

So what is wrong with my approach on #3 then: 10 Red + 5 Blue + 1 Yellow = 16 ?

in order to ensure the correct pill, we maximize the wrong ones

between yellow and blue, yellow has more pills. we choose all these before we choose blue.
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Re: at least - combinatorics - pills [#permalink]

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20 Jan 2008, 21:42
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Yeah in order to get least number of required ones , we need to maximise the wrong ones. 23 is right !
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Re: at least - combinatorics - pills [#permalink]

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24 Jul 2009, 04:50
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I found these uestions super cute!+ they are gr8 to clear one's concept!
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Re: at least - combinatorics - pills [#permalink]

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17 Sep 2009, 18:46
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So.. for 6 and 7 ..

At least one of each color .. since 5 is the lowest number we choose 10R 12Y and 1B ? I didn't quite get this.
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Re: at least - combinatorics - pills [#permalink]

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26 Sep 2009, 23:49
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A box contains
10 red pills
5 blue pills
12 yellow pills.

What is the least number of pills one must extract to ensure at least
1. one blue pill?
2. two blue pills?
3. one blue and one yellow?
4. two blue and one yellow?
5. two blue and two yellow?
6. at least one of each color?
7. at least 3 of each color?

Soln:
1. one blue pill?
Ans: The worst case is if we pick all 10 red pills and 12 yellow pills and then only pick the first blue pill. So the least number of pills to ensure that atleast one blue pill is taken is 23.

2. two blue pills?
Ans: Similar to first question. Since now we need two blue pills. Thus the answer is 24.10 red pills + 12 yellow pills + 2 blue pills

3. one blue and one yellow?
Ans: 10 red pills + 12 yellow pills + 1 blue = 23

4. two blue and one yellow?
Ans: 10 red pills + 12 yellow pills + 2 blue = 24

5. two blue and two yellow?
Ans: 10 red pills + 12 yellow pills + 2 blue = 24

6. at least one of each color?
Ans: 10 red pills + 12 yellow pills + 1 blue = 23

7. at least 3 of each color?
Ans: 10 red pills + 12 yellow pills + 3 blue = 25
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Re: at least - combinatorics - pills [#permalink]

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29 Sep 2009, 02:19
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The questions are tricky and fun at the same time.

I guess some are making confusing because of the wording. The question says

"What is the least number of pills one must extract to ensure at least"
So, we should consider the worst case scenario.

If the question would had asked 'What is the least number of pills one should extract to ensure one blue marbel and so and so...........
Then it might have been the best case scenario.....(I may be wrong )
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Re: at least - combinatorics - pills [#permalink]

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02 Jan 2010, 08:35
I think question should ask "MAX or Most" rather than "Least", for worst case scenario.
What is the max number of pills one must extract to ensure at least ?
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Re: at least - combinatorics - pills [#permalink]

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02 Jan 2010, 09:04
As tashu just pointed out, I also think the word "least" makes the whole question very ambiguous.
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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18 Aug 2013, 10:51
One of my friend was asked a similar question in a job interview and he replied - "One" - interviewer asked how - and he said that "I am lucky so i will get it in first pick and would not wait for X picks (x=real solution))
Interviewer liked his boldness and presence of mind. And he was selected.
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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19 Aug 2013, 10:39
These questions are easy, but scares me allot as there is no direct formula to rely on or leave rest of the effort on well versed algorithms of addition subtraction or division, really it needs alert brain with no open holes in thought process to ignore any possibility or to miss any scenario. Its more like critical reasoning
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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20 Aug 2013, 04:55
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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07 Sep 2014, 23:20
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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30 Oct 2014, 03:15
For question 3, wouldn't the least amount be if you removed all red and all blue first to get at least 1 blue and 1 yellow? Meaning the least amount to ensure 1 blue and 1 yellow = 10 + 5 +1 ...?
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Re: A box contains 10 red pills 5 blue pills 12 yellow [#permalink]

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30 Oct 2014, 03:36
Teslindo wrote:
For question 3, wouldn't the least amount be if you removed all red and all blue first to get at least 1 blue and 1 yellow? Meaning the least amount to ensure 1 blue and 1 yellow = 10 + 5 +1 ...?

For such questions you should consider the worst case scenario. The worst case scenario for question 3 (at least one blue and one yellow) would be if we pick all 10 red pills and all 12 yellow pills. In such case we still won't have at least one blue and one yellow. Next, pick however, would give us blue pill, so we would have at least one blue and one yellow. So, the correct answer is 10 + 12 + 1 = 23.

Check other Worst Case Scenario Questions in our Special Questions Directory.

Hope it helps.
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Re: A box contains 10 red pills 5 blue pills 12 yellow   [#permalink] 30 Oct 2014, 03:36

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