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In an election for class president, each of 32 students vote

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In an election for class president, each of 32 students vote  [#permalink]

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New post 25 Mar 2014, 15:49
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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?

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Re: In an election for class president, each of 32 students vote  [#permalink]

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New post 25 Mar 2014, 19:19
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We are given that A + B + C = 32

(1) B = 9
A + C = 23

B can never have the most votes. If A, for example, has 8 votes, C > B. Sufficient.

(2) C = 13
A + B = 19

B may be greater than, less than or equal to 13. Not sufficient.

The answer is A.
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Re: In an election for class president, each of 32 students vote  [#permalink]

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New post 25 Mar 2014, 22:04
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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Re: In an election for class president, each of 32 students vote  [#permalink]

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New post 26 Mar 2014, 01:24
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?


This is a copy of GMAT Prep's question:
Quote:
Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast?

(1) Candidate F received 11 of the votes.
(2) Candidate H received 14 of the votes.


Discussed here: each-person-on-a-committee-with-40-members-voted-for-exactly-129999.html

Hope it helps.
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Re: In an election for class president, each of 32 students vote  [#permalink]

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New post 26 Apr 2018, 08:32
VeritasPrepKarishma Bunuel chetan2u niks18 gmatbusters

Quote:
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.


Total number of votes - 32
Did B receive maximum votes?

Quote:
(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.


I did not understand highlighted part in sol. Can you please elaborate?
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In an election for class president, each of 32 students vote  [#permalink]

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New post 26 Apr 2018, 08:47
adkikani wrote:
(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.


I did not understand highlighted part in sol. Can you please elaborate?




It just says that It doesn't matter how we divide 23 votes between A and C, one of them will always be getting more than 9 votes. hence making it sure that B is not the highest Vote getter.
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Re: In an election for class president, each of 32 students vote  [#permalink]

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New post 27 Apr 2018, 04:29
Hii
It is a general procedure to minimize the greatest term when the sum of terms given, the min value of greatest term is when all the terms are equal to mean.

It can be noted that if there is any term lower than mean, there would be a term greater than mean to compensate for the same.
So, this is the required configuration.
adkikani wrote:
VeritasPrepKarishma Bunuel chetan2u niks18 gmatbusters

Quote:
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.


Total number of votes - 32
Did B receive maximum votes?

Quote:
(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.


I did not understand highlighted part in sol. Can you please elaborate?

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Re: In an election for class president, each of 32 students vote &nbs [#permalink] 27 Apr 2018, 04:29
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