• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 9 posts ] 
Author Message
 Post subject: GMAT Fractions
PostPosted: Tue Apr 09, 2013 11:58 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
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

(D) The trick to this question is that the number of Icelandic ponies cannot be fractional. It must be an integer.
The number of Icelandic ponies is:
(2/3) × (5/6) × total number of ponies, or
10/18 × total number of ponies.

9 is the smallest positive integer that yields another integer when multiplied by 5/9, and all multiples of 9 will yield a whole number of Icelandic ponies.

However, the number of ponies must also be a multiple of 6 so that the number of ponies with horseshoes is an integer. If there were only 9 ponies, the number of ponies with horseshoes would be:
(5/6) × 9 = 15/2. This is impossible.

The least common multiple of 6 and 9 is 18, so there are 18 ponies at minimum.

If there are 18 ponies, then there must be 18 + 3 = 21 horses. Since 18 + 21 = 39, the minimum number of horses and ponies on the ranch is 39.

The correct answer is choice (D).
----------
The answer can also be 21 (12+9). i.e. 12 horses and 9 ponies. if there are 9 ponies,the total no.of iceland ponies will be 10/18 x 9 = 5 ponies. So combined no. of animals shall be 21(minimum).


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:02 pm 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 456
If there were 9 ponies, then the number of the ponies with horseshoes would be 9 × 5/6 = 15/5 = 7.5. That is the fractional value and can NOT be true.

The key to solve this problem is to keep in mind that all the values must NOT be fractional: the number of the ponies with horseshoes and the number of the ponies with horseshoes from Iceland.


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:02 pm 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
Could you please explain this question more in detail?

Thank You


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:03 pm 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 456
questioner wrote:
Could you please explain this question more in detail?
When you are confused with an explanation, think which logical step you are exactly confused with.

For example, you can be confused with any of these logical steps:
- "The trick to this question is that the number of Icelandic ponies cannot be fractional. It must be an integer."

- "The number of Icelandic ponies is: (2/3) × (5/6) × total number of ponies"

- "9 is the smallest positive integer that yields another integer when multiplied by 5/9"

- "all multiples of 9 will yield a whole number of Icelandic ponies"

- " the number of ponies must also be a multiple of 6 so that the number of ponies with horseshoes is an integer."

- " If there were only 9 ponies, the number of ponies with horseshoes would be: (5/6) × 9 = 15/2. This is impossible."

- "The least common multiple of 6 and 9 is 18, so there are 18 ponies at minimum."

- "If there are 18 ponies, then there must be 18 + 3 = 21 horses. Since 18 + 21 = 39, the minimum number of horses and ponies on the ranch is 39."


When you know which logical step is confusing, you'll be able to look at it more precisely. In many cases you'll find the answer on your own. If not, I would be able to help you. But I can't help you if I don't know what it is that you don't understand. There are many options: fractions are not clear to you, you don't know how to calculate the LCM, you do not understand why we calculate the LCM, you do not understand why the numbers must be integers, etc.

So please, specify, what exactly is NOT clear to you and I'll be able to help. For now, I can only suggest that you plug in some values and see what happens. For example:

If there are 4 ponies, then there are 3 1/3 ponies with horseshoes, and 2 2/9 ponies with horseshoes are from Iceland.

If there are 6 ponies, then there are 5 ponies with horseshoes, and 3 1/3 ponies with horseshoes are from Iceland.

If there are 18 ponies, then there are 15 ponies with horseshoes, and 10 ponies with horseshoes are from Iceland.

If there are 36 ponies, then there are 30 ponies with horseshoes, and 20 ponies with horseshoes are from Iceland.


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:03 pm 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
It is a very good question indeed.


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:04 pm 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
Can the answer be B?


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 12:10 pm 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 456
questioner wrote:
Can the answer be B?
Suppose the answer is B. Then there are 12 horses and 9 ponies on the ranch (because "there are 3 more horses than ponies").

If there are 9 ponies, then there must be 9 × (5/6) ponies with horseshoes. But 9 × (5/6) = 7.5, which is fractional, can not be the number of ponies with horseshoes! It is the contradiction with the question statement, thus 21 does NOT fit as an answer.

The key to solve this problem is to keep in mind that all the values must NOT be fractional: the number of ponies with horseshoes and the number of ponies with horseshoes from Iceland.


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Thu Apr 11, 2013 11:54 pm 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 480
Is this problem missing a qualifier for the ponies? It seems the info about shoes and Iceland are irrelevant. It's only asking for horses and ponies combined, right? I would think the solution would be Total = subtract 3 and divide by two. B creates the smallest whole number. What am I missing on this question? Thanks


Top
 Profile  
 
 Post subject: Re: GMAT Fractions
PostPosted: Fri Apr 12, 2013 12:06 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 456
Quote:
It seems the info about shoes and Iceland are irrelevant.
It is very important here.

Quote:
I would think the solution would be Total = subtract 3 and divide by two. B creates the smallest whole number.
If the total number of ponies and horses was 21, then there would be 12 horses and 9 ponies. But let's go further. There would be

(5/6) × 12 = 10 ponies with horseshoes
and
(2/3) × 10 = 6 2/3 ponies with horseshoes from Iceland.

The number of ponies with horseshoes from Iceland cannot be fractional! Thus B is not the correct answer.

That is why the given information (fractions) about the groups of ponies is important. Above you may find the explanation of how we make sure those groups are not fractional numbers.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 9 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.