January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one. January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 04 Aug 2013
Posts: 96
Location: India
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)

A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
Updated on: 15 Oct 2014, 05:56
Question Stats:
70% (02:41) correct 30% (02:57) wrong based on 148 sessions
HideShow timer Statistics
A certain farm has a group of sheep, some of which are rams (males) and the rest ewes (females). The ratio of rams to ewes on the farm is 4 to 5. The sheep are divided into three pens, each of which contains the same number of sheep. If the ratio of rams to ewes in the first pen is 4 to 11, and if the ratio of rams to ewes in the second pen is the same as that of rams to ewes in the third, which of the following is the ratio of rams to ewes in the third pen? A. 8/7 B. 2/3 C. ½ D. 3/12 E. 1/6
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by anceer on 15 Oct 2014, 05:36.
Last edited by Bunuel on 15 Oct 2014, 05:56, edited 1 time in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 52390

Re: A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
15 Oct 2014, 06:12
anceer wrote: A certain farm has a group of sheep, some of which are rams (males) and the rest ewes (females). The ratio of rams to ewes on the farm is 4 to 5. The sheep are divided into three pens, each of which contains the same number of sheep. If the ratio of rams to ewes in the first pen is 4 to 11, and if the ratio of rams to ewes in the second pen is the same as that of rams to ewes in the third, which of the following is the ratio of rams to ewes in the third pen?
A. 8/7 B. 2/3 C. ½ D. 3/12 E. 1/6 The ratio of rams to ewes on the farm is 4 to 5 > rams:ewes = 4x:5x > total sheep = 9x; The sheep are divided into three pens, each of which contains the same number of sheep > each pen contains 3x sheep. The ratio of rams to ewes in the first pen is 4 to 11 > 4y:11y > sheep in in the first pen = 15y. We know that each pen contains 3x sheep, thus 3x = 15y > x = 5y. From rams:ewes = 4x:5x, we have rams:ewes = 20y:25y. Together in the second and third pins there are (20y  4y) =16y rams and (25y  11y) = 14y ewes, so 8y rams and 7y ewes in each. Ratio = 8y:7y = 8:7. Answer: A. Or you can simply plug numbers, foir example, assume that there are 45 (should be a multiple of 9) sheep and proceed.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
11 Jan 2017, 19:26
Since the ratio of rams to ewes in the first pen is 4:11, let the number of rams in the first pen be 4x and the number of ewes be 11x. Let r be the number of rams in the second pen and let e be the number of ewes in the second pen. Since the number of sheep in each pen is the same, we can construct the following equation: 4x + 11x = r + e, or 15x = r + e. Since the number of sheep in each pen is the same, we know that the number of rams in the second and third pens together is 2r and the number of ewes in the second and third pens together is 2e. Therefore, the total number of rams is 4x + 2r. The total number of ewes is 11x + 2e. Since the overall ratio of rams to ewes on the farm is 4:5, we can construct and simplify the following equation: We can find the ratio of r to e by setting the equations we have equal to each other. First, though, we must multiply each one by coefficients to make them equal the same value: Since both equations now equal 120x, we can set them equal to each other and simplify: The correct answer is A.
Attachments
calculation.PNG [ 13.88 KiB  Viewed 1829 times ]
_________________
Thanks & Regards, Anaira Mitch



Director
Joined: 26 Oct 2016
Posts: 636
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
11 Jan 2017, 19:38
Another approach : It is important to remember that if the ratio of one group to another is x:y, the total number of objects in the two groups together must be a multiple of x + y. So since the ratio of rams to ewes on the farm is 4 to 5, the total number of sheep must be a multiple of 9 (4 parts plus 5 parts). And since the ratio of rams to ewes in the first pen is 4 to 11, the total number of sheep in the first pen must be a multiple of 15 (4 parts plus 11 parts). Since the number of sheep in each pen is the same, the total number of sheep must be a multiple of both 9 and 15. If we assume that the total number of sheep is 45 (the lowest common multiple of 9 and 15), the number of rams is 20 and the number of ewes is 25 (ratio 4:5). 45/3 = 15, so there are 15 sheep in each pen. Therefore, there are 4 rams and 11 ewes in the first pen (ratio 4:11). This leaves 20  4 = 16 rams and 25  11 = 14 ewes in the other two pens. Since the second and third pens have the same ratio of rams to ewes, they must have 16/2 = 8 rams and 14/2 = 7 ewes each, for a ratio of 8:7 or 8/7.
_________________
Thanks & Regards, Anaira Mitch



VP
Joined: 07 Dec 2014
Posts: 1152

A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
21 Jan 2018, 20:53
anceer wrote: A certain farm has a group of sheep, some of which are rams (males) and the rest ewes (females). The ratio of rams to ewes on the farm is 4 to 5. The sheep are divided into three pens, each of which contains the same number of sheep. If the ratio of rams to ewes in the first pen is 4 to 11, and if the ratio of rams to ewes in the second pen is the same as that of rams to ewes in the third, which of the following is the ratio of rams to ewes in the third pen?
A. 8/7 B. 2/3 C. ½ D. 3/12 E. 1/6 let r=rams in pen 3 e=ewes in pen 3 15s=total sheep in pen 1 r+e=15s r+e is a multiple of 15 plugging in choice A, assume r+e=8 rams+7 ewes=15 sheep pen 1 must also contain 15 sheep: 4 rams+11 ewes thus, total farm rams/ewes ratio=20/25=4/5 A



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8805
Location: Pune, India

Re: A certain farm has a group of sheep, some of which are rams (males) an
[#permalink]
Show Tags
21 Jan 2018, 23:14
anceer wrote: A certain farm has a group of sheep, some of which are rams (males) and the rest ewes (females). The ratio of rams to ewes on the farm is 4 to 5. The sheep are divided into three pens, each of which contains the same number of sheep. If the ratio of rams to ewes in the first pen is 4 to 11, and if the ratio of rams to ewes in the second pen is the same as that of rams to ewes in the third, which of the following is the ratio of rams to ewes in the third pen?
A. 8/7 B. 2/3 C. ½ D. 3/12 E. 1/6 Use weighted averages. You have a "total population" which you have split. This should remind you of weighted averages. Concentration of rams in total population = 4/9 Concentration of rams in first pen = 4/15 Concentration of rams in second and third pens combined = x (same concentration in both pens) Since number of sheep in each pen is the same, the weight of first pen:second and third combined = 1:2 1/2 = (x  4/9)/(4/9  4/15) 1/2 *(4/3)*(2/15) + 4/9 = x 8/15 = x Ratio of rams:ewes = 8:7 Answer (A)
_________________
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 >




Re: A certain farm has a group of sheep, some of which are rams (males) an &nbs
[#permalink]
21 Jan 2018, 23:14






