enigma123 wrote:

In an election for class president, each of 32 students voted for exactly one candidate, Ann, Bob or Carl. Did Bob receive the most votes?

(1) Bob received 9 votes.

(2) Carl received 13 votes.

Any idea how to solve this question guys please?

Total number of votes - 32

Did B receive maximum votes?

(1) Bob received 9 votes.

B received 9 votes so we are left with 32 - 9 = 23 votes to be split between A and C. Obviously, it is possible to split them in 20-3 such that one of A or C gets max votes. Is it possible to split them in such a way that B gets max votes? Even if we try to give them equal number of votes, we will need to split them as 11-12. There is no way we can split the 23 votes such that neither A nor C gets more than 9 votes. Hence we can be sure that B DID NOT get maximum votes. You have a definite 'No' answer and hence this alone is sufficient.

(2) Carl received 13 votes.

C received 13 votes so we are left with 19 votes to split between A and B. It is possible that B got all 19 and hence did get max number of votes. It is also possible that A got all 19 or A and B got 10 - 9 votes each etc. Hence we don't know whether B got max votes or not. Not sufficient.

Answer (A)

Tip: Establish a base and then look for extreme cases. I have discussed this strategy in a post:

http://www.veritasprep.com/blog/2014/01 ... base-case/
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