GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 20:30

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58381
In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

02 Aug 2017, 23:49
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:58) correct 26% (01:39) wrong based on 147 sessions

HideShow timer Statistics

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

_________________
Intern
Joined: 05 Mar 2017
Posts: 4
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 02:49
1
4th person -1 vote
This is the only order in which Jill can get max votes
So ans is A

Sent from my iPad using GMAT Club Forum
Manager
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 04:07
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.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 04:17
Bunuel wrote:
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

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)

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)

Here are some posts on Max-Min strategies:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... base-case/
https://www.veritasprep.com/blog/2014/0 ... -extremes/
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 04:29
VeritasPrepKarishma wrote:
Bunuel wrote:
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

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)

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)

Here are some posts on Max-Min strategies:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... base-case/
https://www.veritasprep.com/blog/2014/0 ... -extremes/

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.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 05:39
1
kumarparitosh123 wrote:
VeritasPrepKarishma wrote:
Bunuel wrote:
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

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)

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)

Here are some posts on Max-Min strategies:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... base-case/
https://www.veritasprep.com/blog/2014/0 ... -extremes/

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.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 06:40
VeritasPrepKarishma wrote:
kumarparitosh123 wrote:
VeritasPrepKarishma wrote:
[quote="Bunuel"]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

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)

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)

Here are some posts on Max-Min strategies:
https://www.veritasprep.com/blog/2014/0 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... base-case/
https://www.veritasprep.com/blog/2014/0 ... -extremes/

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.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

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.[/quote]
Agreed ..
Thanks a lot .

I must take utmost care while reading.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
Intern
Joined: 01 Aug 2017
Posts: 2
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

03 Aug 2017, 06:49
1
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 =?

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

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

09 Aug 2017, 12:47
1
Bunuel wrote:
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

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.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior SC Moderator
Joined: 22 May 2016
Posts: 3549
In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

09 Aug 2017, 17:54
Bunuel wrote:
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

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.

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Intern
Joined: 16 Jul 2017
Posts: 1
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

09 Aug 2017, 21:52
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

Kudos if you think this is right!
Senior SC Moderator
Joined: 22 May 2016
Posts: 3549
In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

10 Aug 2017, 06:52
nikhilsk wrote:
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

Kudos if you think this is right!

Jill received the third highest number of votes. I think you interpreted that incorrectly. Two people got MORE votes than she.

"First [highest]" candidate in your scenario gets the 13 votes. Does that make sense?
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Non-Human User
Joined: 09 Sep 2013
Posts: 13208
Re: In a class election, 25 students each cast one vote for one of four ca  [#permalink]

Show Tags

15 Oct 2018, 20:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In a class election, 25 students each cast one vote for one of four ca   [#permalink] 15 Oct 2018, 20:58
Display posts from previous: Sort by