M10-24

Question

A box contains 10 tablets of Medicine A and 15 tablets of Medicine B. What is the minimum number of tablets that need to be removed from the box to guarantee that at least two tablets of each type are among the ones extracted?

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

Show Answer

Official Answer

C

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

Bunuel · Accepted Answer

Official Solution:

A box contains 10 tablets of Medicine A and 15 tablets of Medicine B. What is the minimum number of tablets that need to be removed from the box to guarantee that at least two tablets of each type are among the ones extracted?

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

Show Answer

Official Answer

C

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

The worst-case scenario would occur if we remove all 15 tablets of medicine B first. In this scenario, we would still not have any tablets of medicine A. However, the next two tablets we remove must be of Medicine A. Therefore, to  guarantee  that at least two tablets of each type will be taken, we should remove a minimum of  15+2=17  tablets.

Answer: C

shettyshruthi · Answer

Why isnt it 12?

Bunuel · Answer

We need  at least  2 tablets of A and  at least  2 tablets of B. With 12 picks we  could  have a case when we picked ALL 12 tablets of B (since there are 15 of them) and thus the condition will be violated.

Check other  Worst Case Scenario Questions  from our  Special Questions Directory  to practice.

ENEM · Answer

Hi,

is there a chapter on min/max problems on gmatclub maths theory book?

Bunuel · Answer

No. But you c an check the questions. DS: https://gmatclub.com/forum/search.php?s ... &tag_id=42 PS: https://gmatclub.com/forum/search.php?s ... &tag_id=63 Hope it helps.

ENEM · Answer

thanks Bunuel. Why is the answer not 4? As per my understanding, it asks us the least number of tablets that can be extracted and there should be two of each type, so in that case answer should be 4. Please help.

I did check the questions you mentioned but that doesn't give me any insight into what's wrong in my understanding of this question.

Regards,

Bunuel · Answer

We need to     guarantee     that at least two tablets of each kind are among the extracted. For 4 picks there is no guarantee that at least two tablets of each kind are among the extracted. What if all 4 are of medicine A or all 4 are of medicine B or 3 are of one medicine and 1 is of another?

DrHuber · Answer

(C). To ensure that at least two tablets of each kind are among the extracted, we need to consider the worst-case scenario. Let's assume that we initially pick all the tablets of medicine B, ie 15, and then start picking tablets of medicine A. In the worst-case scenario, we would need to pick all 15 tablets of medicine B. After that, we can start picking tablets of medicine A. To guarantee that we have at least two tablets of medicine A, we need to pick two additional tablets. Therefore, the minimum number of tablets that should be taken is 15 (medicine B) + 2 (medicine A) = 17

So, the correct answer is C. 17 tablets.

So, the correct answer is C. 17 tablets.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

SBD98 · Answer

Hi Bunuel,

I have a confusion. For example: if I pick all 10 tablets of A first, then pick 2 tablets of B from the box, the minimum number of tablets removed would be 12. In this case, I follow the condition of picking at least 2 tablets of each type of medicine. So, why 12 isn't the answer?

Bunuel · Answer

The reason 12 isn't the correct answer is that it depends on a specific order of removal (all 10 of A first, then 2 of B). The question asks for a number that  guarantees  at least two of each type, regardless of the order. This doubt has been addressed in the thread, and for further practice, you can refer to other  Worst Case Scenario Questions  from our  Special Questions Directory  to practice.

Bunuel · Answer

To elaborate further, it's important to recognize that the tablets can be removed in many different orders. Ideally, the best case scenario to meet the requirement of removing at least two tablets of each type would involve immediately removing 2 tablets of Medicine A and 2 tablets of Medicine B. However, this specific order of removal is not guaranteed. What we need to determine is a number of draws that, regardless of the order of removal, will always ensure that at least two tablets of each type are extracted. Hence, to guarantee that at least two tablets of each type are removed under any sequence, it becomes necessary to consider the worst-case scenario, which would be most unfavorable removing order.

Vikramaditya00 · Answer

I think this is a  high-quality  question and I agree with explanation.

bumpbot · Answer

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M10-24

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