Each person on a committee with 40 members voted for exactly one of 3

Question

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.

Bunuel · Accepted Answer

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 --> together G and H received 40-11=29 votes, so either one received at least 15 votes, which means that F definitely did not receiv the most votes. Sufficient.

(2) Candidate H received 14 of the votes --> if F=15 and G=11 then F received the most of the votes but if F=13 and G=13 then F did not receiv the most votes. Not sufficient.

Answer: A.

swathimn · Answer

Hi Bunuel,
Statement 1: Candidate F received 11 of the votes --> together G and H received 40-11=29 votes, Cant one of them get 10 and the other 19 ??? or 9 and 20!! That means we cannot say if F received most or least no of votes./???

Bunuel · Answer

The question asks whether F received the most votes from the 40 votes. From (1) F received 11 votes. Now, you cannot split 29 votes received by G and H together, so that F to have the most votes. Therefore the answer to the question whether F received the most votes is NO.

Hope it's clear.

mbaiseasy · Answer

This is testing averages and distribution.
So, we have 40 votes to distribute to 3 candidates. The extreme way to get most votes is to have the other two candidates get just one vote each.
1,1,38
The most conservative way to get most votes is to distribute the votes equally and offset one vote to one candidate to make it the winner. 40/3=13 with a remainder of 1.
13,13,14
Therefore the candidate with the most votes v is like this 14 < v < 39

(1) if Candidate F has 11 then he surely did not get the v we are looking for. 11 could never be a value for the most vote. SUFFICIENT
(2) if Candidate H received 14. 
If distribution is 14,13,13 then H got the most vote and not F.
If distribution is 14,1,25 then Either F or the other got the most vote.
INSUFFICIENT

Answer: A

swathimn · Answer

Thanks Bunuel!! You have been very helpful, All the posts from you are extremely useful!! I just wished there was someone who could show as much interest in verbal as well!! I don really see expert replies in verbal as a result of which you still have lots of doubts especially in reasoning abilities!! Thanks a lot, quant team is doing a great job

sanjoo · Answer

A...

ANS should be yes or no in DS questions.. A ans NO.. it should be the ans.

krrish · Answer

stmt1: f got 11 votes, 
given 40 votes are cast, remaining 40-11 =29 even if divided equally among others 14, 15 or if one gets 0 even then f is not the max votes geter so A. is suff
stmt2: it saygs H got 14 remaining is 26, now f has cnances which we can't predict. so D is rules out..

final answers A

Bunuel · Answer

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mathivanan · Answer

From state(1) the answer is no because for most votes, F should get minimum 14 votes.
From state(2), we cannot answer because F and G can share the remaining 26 votes in any ratio.
therefore the answer is (A)

ksrutisagar · Answer

Given : F + G + H = 40

St 1 : F = 11

So, G + H = 29

To minimize both G and H under the above constraint,

G= 15 , H = 14 or G = 14, H = 15

In either case F did not receive the most votes

Definite No

Sufficient

St 2 : H = 14

Case 1 : F = 15, G = 11 Yes

Case 2 : F = 11, G = 15 No

Not Sufficient

Choice A

yashikaaggarwal · Answer

F+G+H = 40 => (Given)

statement 1: F received 11 votes,
case 1: let suppose other two received near about same votes. 14,15 
Then F votes are least among all candidates.

case 2: let suppose one of them get less vote than F, supposedly 9
other will receive 40-9-11=20
Then also F votes are not greatest among all.
(sufficient)

Statement 2: : H received 14 votes,
case 1: let suppose other two received near about same votes. 13,13
Then F votes are not greatest among all candidates. (not satisfying)

case 2: let suppose G get less vote than H, supposedly 10
F will receive 40-10-14=16
Then F votes are greatest among all. (satisfying)

case 3: let suppose F get less vote than H, supposedly 10
Then F votes are not greatest among all. (not satisfying)
(Insufficient)

Answer is A

nick1816 · Answer

Statement 1-  Since  11 < \frac{40}{3} , Candidate F didn't receive the highest number of votes.

Sufficient

Statement 2-  Candidate H received 14 of the votes. So, F can receive from 0 to 26 number of votes. We can't have a definite answer.

Insufficient

Hoozan · Answer

Each person voted for EXACTLY one of the 3 candidates so we could simplify the question to:  Is F > 20 ?
(1) F = 11 - suff
(2) F could be as small as 12 and as large as 25 - insuff

Correct Choice:  (A)

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Each person on a committee with 40 members voted for exactly one of 3

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