Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A box contains 10 red pills 5 blue pills 12 yellow [#permalink]
07 Dec 2007, 11:03

2

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

79% (02:32) correct
21% (01:57) wrong based on 23 sessions

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?

Re: at least - combinatorics - pills [#permalink]
07 Dec 2007, 12:03

4

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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

Re: at least - combinatorics - pills [#permalink]
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.

Re: at least - combinatorics - pills [#permalink]
26 Sep 2009, 23:49

3

This post received KUDOS

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

Re: at least - combinatorics - pills [#permalink]
29 Sep 2009, 02:19

1

This post received KUDOS

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 )

Re: at least - combinatorics - pills [#permalink]
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 ?

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

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

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

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]
20 Aug 2013, 04:55

Expert's post

3

This post was BOOKMARKED

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]
07 Sep 2014, 23:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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

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

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.

Originally, I was supposed to have an in-person interview for Yale in New Haven, CT. However, as I mentioned in my last post about how to prepare for b-school interviews...

Hi Starlord, As far as i'm concerned, the assessments look at cognitive and emotional traits - they are not IQ tests or skills tests. The games are actually pulled from...

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...

The 2015 Pan American Games and more than 6,000 athletes have come to Toronto. With them they have brought a great positive vibe and it made me think...