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A herd of 33 sheep is sheltered in a barn with 7 stalls 12 Sep 2014, 07:21
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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.
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C
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Bunuel
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A herd of 33 sheep is sheltered in a barn with 7 stalls 12 Sep 2014, 08:09
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chetan86
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.
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Each statement alone is clearly insufficient. When taken together we have:

C:E = 2:3 = 10:15.
E:F = 5:2 = 15:6.

C:E:F = 10:15:6.

Since there are total of 33 sheeps, then there must be 10 in C, 15 in E and 6 in F, which totals to 31. So, there are 2 sheeps left for 4 remaining stalls, which means that there must be at least 2 stalls empty. Sufficient.

Answer: C.
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A herd of 33 sheep is sheltered in a barn with 7 stalls 04 Oct 2016, 07:04
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chetan86
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.
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1. we can have C=2, E=3, and have enough for rest to have at least 1. or we can have 12 and 18, which is equal to 30, and 3 are left, not enough.
1 alone is not sufficient.

2. we can have 5 in E and 2 in F, and sufficient number of sheep to get in every single stall.
we can have 20 in E and 8 in F, total 28, and 5 are left. we can have 1 in each of them, or we can have 1 in only one.
2 alone is not sufficient.

1+2
minimum number of sheep in E must be 15. in this case, C must have 10, and F - 6. total 31. we have 2 sheep left and 4 stalls. we can give a definite answer now.

C.
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A herd of 33 sheep is sheltered in a barn with 7 stalls 25 Jun 2019, 06:00
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C:E=2:3
E:F=5:2
C:E:F=10:15:6
and the total of this is 31, we are left with 2 sheeps and 4 places and therefore not every place has one sheep and hence C.
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A herd of 33 sheep is sheltered in a barn with 7 stalls 27 Jun 2019, 04:31
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This is a moderately difficult question on interpretation of ratios. Bear in mind that this is a ‘Yes No’ type of DS question. So, getting a ‘No’ is also an accepted answer.

From statement I alone, we have the ratio of sheep in stalls C and E but not the others. Therefore, this statement is insufficient to answer the main question with a definite YES or a definite NO.

From statement II alone, we have the ratio of sheep in stalls E and F, but not the others. Again, this is sufficient to give a unique answer to the main question.

When we combine statements I and II, we can find out the ratio of C:E:F to be 10:15:6. This ratio refers to the number of sheep in the respective stalls. Therefore, the smallest possible values for the actual number of sheep in these stalls are 10, 15 and 6.
This means, these 3 stalls have a total of 31 sheep. We are left with 4 stalls but only 2 sheep. Even if we accommodate one sheep each in 2 stalls, 2 stalls will be left empty.

“Is there at least one sheep in every stall?” – From the above, the answer is a clear NO.
So, this data is sufficient and the correct answer option is C.

When you arrive at the ratio 10:15:6, there are two things that will keep running in parallel in your mind:

    A ratio does not represent the actual value always. So numbers in the ratio of 10:15:6 can be (10,15,6) or (20,30,12) and so on.
    Because of the above, can I assume the actual values as 10, 15 and 6?

Clearly, the answer is YES, because of the constraint that the total number of sheep are 33 only.
Hope this helps!
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A herd of 33 sheep is sheltered in a barn with 7 stalls 16 Jun 2024, 05:57
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