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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A herd of 33 sheep is sheltered in a barn with 7 stalls ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A herd of 33 sheep is sheltered in a barn with 7 stalls A herd of 33 sheep is sheltered in a barn with 7 stalls, each of which is labeled with a unique letter from A to G, inclusive. Is there at least one sheep in every stall? (1) The ratio of the number of sheep in stall C to the number of sheep in stall E is 2 to 3. (2) The ratio of the number of sheep in stall E to the number of sheep in stall F is 5 to 2. Is there any statement that is sufficient? Why or why not? OA C ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi lheiannie07, We're told that a herd of 33 sheep is sheltered in a barn with 7 stalls, and each of the stalls is labeled with a unique letter from A to G, inclusive. We're asked if there is at least one sheep in every stall. This is a YES/NO question. We can solve it by TESTing VALUES. 1) The ratio of the number of sheep in Stall C to the number of sheep in Stall E is 2 to 3. Fact 1 tells us that the number of sheep in Stall C is a multiple of 2 and the number of sheep in Stall E is an equivalent multiple of 3. IF.... Stall C = 12 sheep and Stall E = 18 sheep, then there are only 3 sheep for the other 5 stalls - and the answer to the question is NO. Stall C = 2 sheep and Stall E = 3 sheep, then there are 28 sheep for the other 5 stalls - so the answer could be YES. Fact 1 is INSUFFICIENT. 2) The ratio of the number of sheep in stall E to the number of sheep in stall F is 5 to 2. Fact 2 tells us that the number of sheep in Stall E is a multiple of 5 and the number of sheep in Stall F is an equivalent multiple of 2. IF.... Stall E = 20 sheep and Stall F = 8 sheep, then there are 5 sheep for the other 5 stalls - so if we put 1 sheep in each of the remaining Stalls, then the answer to the question is YES (and if we don't put 1 in each of the remaining Stalls, then the answer is NO). Fact 2 is INSUFFICIENT. Combined, we know... -The number of sheep in Stall C is a multiple of 2 and the number of sheep in Stall E is an equivalent multiple of 3. -The number of sheep in Stall E is a multiple of 5 and the number of sheep in Stall F is an equivalent multiple of 2. -Combining these Facts.... -The number of sheep in Stall E MUST be a multiple of 15, so.... -The number of sheep in Stall C MUST be a multiple of 10 and.... -The number of sheep in Stall F MUST be a multiple of 6 This accounts for 31 of the 33 sheep, leaving just 2 sheep for the remaining 4 stalls. By extension, the answer to the question is ALWAYS NO. Combined, SUFFICIENT Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2666 messages Followed by: 125 members Upvotes: 1153 GMAT Score: 770 Top Reply lheiannie07 wrote: A herd of 33 sheep is sheltered in a barn with 7 stalls, each of which is labeled with a unique letter from A to G, inclusive. Is there at least one sheep in every stall? (1) The ratio of the number of sheep in stall C to the number of sheep in stall E is 2 to 3. (2) The ratio of the number of sheep in stall E to the number of sheep in stall F is 5 to 2. Is there any statement that is sufficient? Why or why not? OA C Statement 1: Clearly insufficient. You could have exactly 2 sheep in C, exactly 3 sheep in E and the remaining 28 sheep in A, in which case, NO, there's not one sheep in every stall. Or you could have 2 sheep in C, 3 sheep in E, 1 each in A, B, D, and F, and the remaining sheep in G, in which case YES, there'd be at least one sheep in each stall. Statement 2: Again insufficient. Same logic. Once you have 5 sheep in E and 2 sheep in F, the remaining 26 sheep can be distributed however we'd like Together: Now it gets interesting. Statement 1 dictates that the number of sheep in stall E must be a. multiple of 3. Statement 2 dictates that the number of sheep in stall E must also be a multiple of 5. So if the number of sheep in E must be a multiple of both 3 and 5, then it must be a multiple of 15. So the fewest sheep one could have in E would be 15. If there are 15 Sheep in E, there'd be 10 sheep in C. (10:15 = 2:3) If there are 15 sheep in E, there'd be 6 sheep in F. (15:6 = 5:2) If there are 15 in E, 10 in C, and 6 in F, we've accounted for 31 sheep, leaving us only 2 sheep remaining for the remaining 4 stalls. Clearly, we cannot have a sheep in every stall, and thus the answer is a definitive NO. Together the statements are sufficient to answer the question. The answer is C. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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