A herd of 33 sheep is sheltered in a barn with 7 stalls

[BTGmoderatorDC]

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

[DavidG@VeritasPrep]

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.

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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

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