A Box Contains 10 Tablets of Medicine A and 15 Tablets of Medicine B GMAT Problem Solving

Question: 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?

1. 12
2. 15
3. 17
4. 19
5. 21

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1:

The worst case scenario will be if we remove all 15 tablets of medicine B firstly.

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.

Correct Answer: C

Approach Solution 2:

Atleast 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 atleast 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

This means pick 17 then you have to pick atleast 2 from A as well as atleast 2 from B

Correct Answer: C

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