February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53063

In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
02 Aug 2017, 22:49
Question Stats:
75% (01:57) correct 25% (01:36) wrong based on 136 sessions
HideShow timer Statistics



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, 01:49
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
Sent from my iPad using GMAT Club Forum



Manager
Joined: 02 Nov 2015
Posts: 165

Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
03 Aug 2017, 03:07
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 S850LC using GMAT Club Forum mobile app



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8891
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, 03:17
Bunuel wrote: In a class election, 25 students each cast one vote for one of four candidates for student council. If Jill received the thirdhighest 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) 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 MaxMin strategies: https://www.veritasprep.com/blog/2014/0 ... thegmat/https://www.veritasprep.com/blog/2014/0 ... basecase/https://www.veritasprep.com/blog/2014/0 ... extremes/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 02 Nov 2015
Posts: 165

Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
03 Aug 2017, 03:29
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 thirdhighest 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) 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 MaxMin strategies: https://www.veritasprep.com/blog/2014/0 ... thegmat/https://www.veritasprep.com/blog/2014/0 ... basecase/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 S850LC using GMAT Club Forum mobile app



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8891
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, 04:39
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 thirdhighest 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) 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 MaxMin strategies: https://www.veritasprep.com/blog/2014/0 ... thegmat/https://www.veritasprep.com/blog/2014/0 ... basecase/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 S850LC using GMAT Club Forum mobile appJill 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 02 Nov 2015
Posts: 165

Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
03 Aug 2017, 05:40
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 thirdhighest 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) 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 MaxMin strategies: https://www.veritasprep.com/blog/2014/0 ... thegmat/https://www.veritasprep.com/blog/2014/0 ... basecase/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 S850LC using GMAT Club Forum mobile appJill 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 S850LC 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, 05:49
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
09 Aug 2017, 11:47
Bunuel wrote: In a class election, 25 students each cast one vote for one of four candidates for student council. If Jill received the thirdhighest 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 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 thirdhighest 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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior SC Moderator
Joined: 22 May 2016
Posts: 2491

In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
09 Aug 2017, 16:54
Bunuel wrote: In a class election, 25 students each cast one vote for one of four candidates for student council. If Jill received the thirdhighest 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. Answer A
_________________
To live is the rarest thing in the world. Most people just exist. —Oscar Wilde



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, 20:52
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 4th candidate gets 13 votes
Total votes : 25
Kudos if you think this is right!



Senior SC Moderator
Joined: 22 May 2016
Posts: 2491

In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
10 Aug 2017, 05:52
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 4th candidate gets 13 votes
Total votes : 25
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?
_________________
To live is the rarest thing in the world. Most people just exist. —Oscar Wilde



NonHuman User
Joined: 09 Sep 2013
Posts: 9879

Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
Show Tags
15 Oct 2018, 19:58
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In a class election, 25 students each cast one vote for one of four ca
[#permalink]
15 Oct 2018, 19:58






