In a class election, 25 students each cast one vote for one of four ca

Question

In a class election, 25 students each cast one vote for one of four candidates for student council. If Jill received the third-highest number of votes, and no two candidates received the same number of votes, what is the greatest number of votes she could have received?

A. 7
B. 8
C. 9
D. 10
E. 11

A. 7
B. 8
C. 9
D. 10
E. 11

KarishmaB · Accepted Answer

How to approach such a question: There are 4 candidates. To maximise the votes received by the third one, first of all, I will assume that the fourth one got 0 votes. Now I have to divide 25 votes among 3 people as equally as possible (so that the third one gets as many votes as possible) 25/3 = about 8 So 3 people could have got votes as 9, 8, 8 But no 2 people could have got the same number of votes. So the third person must have got 7 votes (and other two 10, 8) Answer (A) Here are some posts on Max-Min strategies: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... -the-gmat/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... base-case/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... -extremes/

Archit156 · Answer

Answer is 7
1st person -9 votes
2nd person -8 votes 
3rd person(Jill)-7 votes
4th person -1 vote
Total 25 votes
This is the only order in which Jill can get max votes
So ans is A

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kumarparitosh123 · Answer

Let the persons be A, B , J , K, each getting a different no of votes. and let J stand for Jill. And let A get the minimum ad K get the maximum vote.
Since we have to maximise J, we will have to minimise A and B.
So the minimum can be 1 and 2 leaving us with 22. Now maximum J can get is 10 and the other can get 12.

So Anwer should be D.

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kumarparitosh123 · Answer

Mam,
I am still not clear why my solution I wrong. Since it has been mentioned that all for get different votes. Secondly it has been asked that what maximum votes Jill can get ? 
It has also been mentioned that each gets atleast one vote, so how can we assume that the fourth got zeo vote.

Kindly bear with me for my misunderstanding and pls help me.

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KarishmaB · Answer

Jill has the third highest number of votes so there are 2 people who have more votes than her. Also, we are not given that each must get one vote at least.
We are given that "25 students each cast one vote for one of four candidates for student council" - so each of the 25 cast a vote for one of the 4. Now, it is not necessary that each of the 4 must have got at least 1 vote.

kumarparitosh123 · Answer

Jill has the third highest number of votes so there are 2 people who have more votes than her. Also, we are not given that each must get one vote at least.
We are given that "25 students each cast one vote for one of four candidates for student council" - so each of the 25 cast a vote for one of the 4. Now, it is not necessary that each of the 4 must have got at least 1 vote. 
Agreed ..
Thanks a lot .

I must take utmost care while reading.

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jak440 · Answer

Here was my thought process:

We are looking for 3rd place (x # of votes). Each candidate received a different number of votes and we know that it has to be an integer (no partial votes), so the closest she could have been to 2nd place is x+1. Closest to 1st place is x+2.

1st = x+2
2nd = x+1
3rd = x
4th =?
Total votes = 25

Well for 4th place, the worst someone could do is 0. If we do a quick formula and solve for x:

(x+2)+(x+1)+x+0=25
3x+3=25
3x=22
x= 7 1/3

Again, we know that x must be an integer. If we round up and say she got 8 votes, then 2nd place would have 9 and 1st would have 10. That means there were 27 votes.. doesn't work.

We round down and she got 7 votes (2nd got 8, 1st got 9). That totals 24 and we realize then 4th place got 1 vote.

If we want to verify it works out OK, we can quickly say 4th place = 1 vote in our formula above.

3x + 4 = 25
x=7

1st place = 9 votes, 2nd place = 8 votes, 3rd place = 7 votes, and 4th place voted for themselves

Answer: A

JeffTargetTestPrep · Answer

We can let the number of votes Jill received = n. Since we want to maximize the number of her votes, we want to minimize the number of votes the other three candidates received. Since Jill received the third-highest number of votes and no two candidates received the same number of votes, we can let n + 1 = the number of votes the second place candidate received and n + 2 = the number of votes the first place candidate received, while the last place candidate received 0 votes. Thus, we have:

0 + n + (n + 1) + (n + 2) = 25

3n + 3 = 25

3n = 22

n = 7⅓

Of course, n has to be an integer; thus, n must be 7 and it’s the largest integer value n could be. It’s possible that the first place candidate could have received 9 votes, the second place candidate 8 votes, Jill 7 votes, and last place candidate 1 vote, or the first place candidate could have received 10 votes, the second place candidate 8 votes, Jill 7 votes, and last place candidate 0 votes.

We note that Jill could not have received 8 or more votes, because in that case, the second place candidate would have received at least 9 votes and the first place candidate would have received at least 10 votes, but those votes alone exceed 25 votes even if the last place candidate received 0 votes.

Answer: A

generis · Answer

This question is ripe for backsolving.

Start with C. If Jill got 9, and was third highest vote recipient, at the least, second place got 10, and first place got 11. The total is 30. Too many.

Try A. If Jill got 7, second place got at least 8, and first place got at least 9. Total is 24.

No need to check B. Answer A yielded 24. With 8 for Jill, we'd be adding +1 to each of A's numbers, and we only have room for one more vote -- not three.

Answer A

nikhilsk · Answer

Why not E?

1st candidate gets 0 vote
2nd candidate gets 1 vote (since we want to maximize votes for the 3rd candidate)
Now we have to divide 24 votes between 3rd and 4th canddiate which is 11+13
So 3rd candidate (Joe) gets 11 votes
4th candidate gets 13 votes

Total votes : 25

Kudos if you think this is right!

generis · Answer

Jill received the third highest number of votes. I think you interpreted that incorrectly. Two people got MORE votes than she. "First " candidate in your scenario gets the 13 votes. Does that make sense? :-)

bumpbot · Answer

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