1. set contains 2,3,5,7. median = 4. now, say number 'n' is added then the median becomes 1.25 x 4 = 5. so n >= 5. hence answer choice A (n cannot be less than 5)

2. could not understand " what is the least possible that ensures " ... sorry.

3. total correct answers = 50M * .64 = 32M; if after next students attempt total % needs to be 70 then, 50(M+1) * 0.7 = 35M + 35; so next student needs to answer 35M + 35 - 32M = 3M + 35 correctly so ans choice B

In the worst possible scenario, the first 15 tablets will be of kind B . To ensure that there are at least two tablets of each kind we have to take out 17 tablets. The correct answer is C.
However I did not understand this explaination

Ok. That makes sense now. Let's through each answer choice... since we need to know the least value of N, let's start from A which is 12
A. 12, now you could have all type B tablets and none type A tablets. So 12 is not the least number. it should be more than 12

B. 15, now same as A, you could have all 15 of type B and none of type A, so insuff.

C. 17, if you take out 17 tablets, you can have max of 15 type B tablets and 2 of type A tablets. hence 17 tablets will ensure you have at least 2 of each type pf tablets. hence the answer.

ans choices 19 and 21 are also correct but we need least number of tablets to ensure 2 of each type hence 17 wins.

I feel in problems like this you must maximize the max of two no.s to ensure you meet the required condition. maximize type B tablets and add minimum no of type A tablets. you get an answer of 17 hurrrayy

hope this helps..