Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 Feb 2012
Posts: 66
Location: Canada
Concentration: Finance, General Management
GPA: 3.8
WE: Information Technology (Computer Software)

A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
10 May 2012, 06:10
Question Stats:
62% (02:22) correct 38% (02:25) wrong based on 394 sessions
HideShow timer Statistics
A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? A. 18 B. 21 C. 38 D. 39 E. 57
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59590

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
10 May 2012, 06:21
piyushksharma wrote: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A. 18 B. 21 C. 38 D. 39 E. 57 Say there are P ponies on the ranch. Then # of ponies with horseshoes is P*5/6, which means that P must be a multiple of 6; # of ponies from Iceland is (P*5/6)*2/3=P*5/9, which means that P must be a multiple of 9. P to be multiple of both 6 and 9 it should be a multiple of 18. The least positive multiple of 18 is 18 itself, so P(min)=18 and H(min)=18+3=21, so the minimum possible combined number of horses and ponies on the ranch is 18+21=39. Answer: D.
_________________




Intern
Joined: 03 Apr 2012
Posts: 22

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
11 May 2012, 11:57
Bunuel wrote: piyushksharma wrote: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A. 18 B. 21 C. 38 D. 39 E. 57 Say there are P ponies on the ranch. Then # of ponies with horseshoes, which are from Iceland is P*5/6*2/3=P*10/18. So, P must be a multiple of 18. The least positive multiple of 18 is 18 itself, so P(min)=18 and H(min)=18+3=21, so the minimum possible combined number of horses and ponies on the ranch is 18+21=39. Answer: C. Hi Bunuel, I am confused with the question. it states, ranch has horses and ponies and horse= ponies+3. all the information regarding the ponies having horseshoes, isnt it extraneous? becasue the final question, is, what is the minimum # of horses and ponies? it doesnt ask ponies with horseshoes? i came up with 21 based on my understanding. considering your solution, you can reduce p*10/18 to p*5/9, hence p=9 to have mimimum ponies horse = 9+3 = 12 hence total is 12+9 = 21 can you please correct my mistake? thanks in advance jay



Intern
Joined: 12 Oct 2011
Posts: 12

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
11 May 2012, 21:57
Even i got the same answer as 21...pls can some one answer this.



Math Expert
Joined: 02 Sep 2009
Posts: 59590

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
12 May 2012, 02:53
jayaddula wrote: Bunuel wrote: piyushksharma wrote: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A. 18 B. 21 C. 38 D. 39 E. 57 Say there are P ponies on the ranch. Then # of ponies with horseshoes, which are from Iceland is P*5/6*2/3=P*10/18. So, P must be a multiple of 18. The least positive multiple of 18 is 18 itself, so P(min)=18 and H(min)=18+3=21, so the minimum possible combined number of horses and ponies on the ranch is 18+21=39. Answer: C. Hi Bunuel, I am confused with the question. it states, ranch has horses and ponies and horse= ponies+3. all the information regarding the ponies having horseshoes, isnt it extraneous? becasue the final question, is, what is the minimum # of horses and ponies? it doesnt ask ponies with horseshoes? i came up with 21 based on my understanding.
considering your solution, you can reduce p*10/18 to p*5/9, hence p=9 to have mimimum ponies horse = 9+3 = 12 hence total is 12+9 = 21can you please correct my mistake? thanks in advance jay If P=9 as you say then # of ponies with horseshoes would be P*5/6=15/2, which is not possible since it's not an integer. AGAIN: Say there are P ponies on the ranch. Then # of ponies with horseshoes is P*5/6, which means that P must be a multiple of 6; # of ponies from Iceland is (P*5/6)*2/3=P*5/9, which means that P must be a multiple of 9. P to be multiple of both 6 and 9 it should be a multiple of 18. The least positive multiple of 18 is 18 itself, so P(min)=18 and H(min)=18+3=21, so the minimum possible combined number of horses and ponies on the ranch is 18+21=39. Answer: D.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59590

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
16 Jul 2013, 00:13
Bumping for review and further discussion.
_________________



Director
Joined: 17 Dec 2012
Posts: 623
Location: India

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
16 Jul 2013, 01:16
piyushksharma wrote: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A. 18 B. 21 C. 38 D. 39 E. 57 1. 5/6 of the ponies have horseshoes. We know that should be equal to some number of ponies. Since we are talking of ponies that number should be an integer. 2. Similarly 2/3 of 5/6 of ponies i.e., 5/9 of ponies should also be an integer. 3. Conditions (1) and (2) have to be satisfied by the minimum possible number of ponies 4. We have 5/6 of ponies and 5/9 of ponies to be integers. The minimum number of ponies that satisfy both is 18. 5. Therefore, the minimum possible combined number of horses and ponies is 21 + 18 =39
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



Intern
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 48
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14 GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
16 Jul 2013, 01:32
Let H = Number of Horses and P= Number of Ponies, our target is H+P = minimum
Statement 1:  it is given (5/6)P = positive integer, i.e. exactly 5/6 of pony has horseshoe Statement 2:  it is also given (2/3)(5/6)P = positive integer, i.e. 2/3 of statement 1 is from iceland
From above two statements, if P has to be minimum, then it can be derived that P = 18, any number less than 18 will not satisfy both Statement1 and Statement2.
Statement 3:  informs that P+3 = H so if P=18, then H= 21 Hence the minimum combination of H & P is 18+21 = 39. Hence answer is D



Manager
Joined: 13 Dec 2012
Posts: 186

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
16 Jul 2013, 05:26
piyushksharma wrote: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
A. 18 B. 21 C. 38 D. 39 E. 57 Quite tricky. If you are in a hurry and running against time here's what to do. Step 1: Given that there are three more horses than ponies, subtract 3 from all the answer choices. Any one of them that has an even number is going to be the answer since the correct number of ponies multiplied by two go get the total number of numbers (less the 3 we initially subtracted) is even. Answer choices have been narrowed down to B, D or E. Guessing at this stage gives you a higher percentage of guessing right than picking any one of the five randomly. Step 2: Divide the answer gotten in a by 2 to get the likely number of ponies and we have any of the following: B: (213) / 2 = 9 D: (393) / 2 = 18 E: (573) / 2 = 28 Step 3: We have 5/6 of ponies with horseshoes and then 2/3 of ponies with horseshoes from Iceland. That means we have to look for a number that is first divisible by 6 to get 5/6 of a number that is an integer. Only 18 is the possible answer since Options B and E are indivisible by 6. If any other one had been divisible by 6, we would have gone further to check which one is also divisible by 3 after dividing by 6 since we need to know which number will have 2/3 as an integer after dividing by 6. If we had more than one number that met these steps, then we would have gone for the lower number since we were looking for the "minimum possible combined number of horses and ponies".
_________________



Manager
Joined: 18 Oct 2011
Posts: 77
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
17 Jul 2013, 11:17
We want to minimize the number of ponies in order to solve the question. This minimum number of ponies will be added by 3 to get the total # of horses.
I used a trial and error approach here to figure out the # of ponies because the fractions given give us clues as to which numbers to pick. For the ponies to have horseshoes, the number must be divisible by 6. If you use 6 you will end up with 5 poines which is not wholey divisible by 2/3 for the ponies that come from iceland. If you go to the next multiple of six, which is 12, you end up with the same problem > 10 is not wholey divisible by 2/3.
The next multiple of 6 which is 18 works well. You end up with 15 ponies w/horseshoes (5/6 of 18) of which 10 of those ponies (2/3 of 15) come from iceland.
Adding 3 to 18 gives you 21 horses. 21+18 = 39. Answer is D



Intern
Joined: 16 Jun 2013
Posts: 4
Concentration: Technology, Strategy

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
26 Aug 2013, 07:06
how possible it can be a 700level question comparing to some 600700 level questions?



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
18 Dec 2013, 00:08
Let ponies = x, so horses should be x+3 Total no. of ponies & horses (minimum) should be any one of the five choices (18,21,38,39,57) So, 2x + 3 can be anything of (18,21,38,39,57)
Choice A (18), Choice C (38) ruled out as x returns a fraction value
Consider Choice B (21): x = 9; 5/6 of 9 comes to be a fraction, so this option ruled out
Consider Choice D (39): x = 18; 5/6 of 18 = 15 & 2/3 of 15 = 10
As we require to find minimum possible, Answer = D (39)



Manager
Joined: 18 Oct 2013
Posts: 68
Location: India
Concentration: Technology, Finance
Schools: Duke '16, Johnson '16, Kelley '16, Tepper '16, Marshall '16, McDonough '16, Insead '14, HKUST '16, HSG '15, Schulich '15, Erasmus '16, IE April'15, Neeley '15
GMAT 1: 580 Q48 V21 GMAT 2: 530 Q49 V13 GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
20 Dec 2013, 07:21
Hi ,
Bunuel you calculated question correctly but provide answer C which should be D. 3 cheers for your solution.
I used back solving approach rather than attacking from from for easy and less time consuming. .Please find it.
As H=P+3. All answers are (H+P) i.e. total animal in ranch. SO we can check out P which are integers. H+P=P+3 + P=2P+3 A) 18 . P=15/2 .Not Integer. Eliminate B) 21 . P=18/2=9 .If 5/6 Ponies have horse shoe than P should be multiple of 6. It cannot be 9 . Eliminate C) 38 . P=35/2 .Not Integer. Eliminate D) 39 . P=36/2=18 . If 5/6 Ponies have horse shoe than P should be multiple of 6. 18 is multiple of 6 . Correct E) 57 . P=54/2 =27 . If 5/6 Ponies have horse shoe than P should be multiple of 6. It cannot be 27 . Eliminate
Answer is D +1 for me.



Math Expert
Joined: 02 Sep 2009
Posts: 59590

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
20 Dec 2013, 08:13
vikrantgulia wrote: Hi ,
Bunuel you calculated question correctly but provide answer C which should be D. 3 cheers for your solution.
I used back solving approach rather than attacking from from for easy and less time consuming. .Please find it.
As H=P+3. All answers are (H+P) i.e. total animal in ranch. SO we can check out P which are integers. H+P=P+3 + P=2P+3 A) 18 . P=15/2 .Not Integer. Eliminate B) 21 . P=18/2=9 .If 5/6 Ponies have horse shoe than P should be multiple of 6. It cannot be 9 . Eliminate C) 38 . P=35/2 .Not Integer. Eliminate D) 39 . P=36/2=18 . If 5/6 Ponies have horse shoe than P should be multiple of 6. 18 is multiple of 6 . Correct E) 57 . P=54/2 =27 . If 5/6 Ponies have horse shoe than P should be multiple of 6. It cannot be 27 . Eliminate
Answer is D +1 for me. Yes, 39 is answer D not C. Edited the typo. Thank you.
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13727

Re: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
Show Tags
07 Oct 2018, 00:37
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: A ranch has both horses and ponies. Exactly 5/6 of the
[#permalink]
07 Oct 2018, 00:37






