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

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

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, 20:09, edited 2 times in total.

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

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 )

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 ?

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

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18 Aug 2013, 11:51

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. _________________

You'll alwaysmiss 100% of the shots you don't take

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

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19 Aug 2013, 11:39

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 _________________

Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use?| 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

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

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20 Aug 2013, 05:55

Expert's post

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PiyushK wrote:

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

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

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08 Sep 2014, 00:20

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

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30 Oct 2014, 04:15

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 ...?

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

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30 Oct 2014, 04:36

Expert's post

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.

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