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

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

by BTGmoderatorDC » Sun Sep 15, 2019 6:10 pm

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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.

OA C

Source: Manhattan Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Sep 15, 2019 8:55 pm

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Your Answer

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C

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BTGmoderatorDC 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.

OA C

Source: Manhattan Prep
Needless to state that each statement alone is sufficient.

Let's find a common ratio of C, E and F.

C : E : F
2 : 3 : -
- : 5 : 2
----------------
We see that E is common to the ratio C : E and E : F, but E has two values 3 and 5. To make E's value unique, take LCM of 3 and 5 and assign E that value. LCM of 3 and 5 is 15. Thus, E = 15 and C would then be 2*5 = 10, and E would be 2*3 = 6.

The combined ratio of C, E and F is 10 : 15 : 6.

The total of 10, 15 and 6 = 31. We see that 31 is the minimum value of the number of sheep in three stalls C, E and F. Now the remaining number of sheep = 33 - 31 = 2 and the remaining number of empty stalls is 4, so at least 2 stalls would be empty. The answer is no, at least one sheep in NOT there in every stall. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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