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.
