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the National Museum

by CSASHISHPANDAY » Wed Sep 19, 2012 9:26 pm
Before the regime change, the National Museum regularly displayed only one third of the artifacts in its collection; the other two thirds were kept in storage. The National Museum's curator estimates that one seventh to one fifth of the artifacts in the museum's collection disappeared during the regime change. If the National Museum now wishes to display the same number of artifacts as it did before the regime change, and if none of the missing artifacts are recovered, then what is the greatest possible fraction of the artifacts in its collection that the museum can keep in storage?
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by KapilKapoor » Wed Sep 19, 2012 10:32 pm
Hi,

Assume the museum has x artifacts.

x/3 = display
2x/3 = storage

x/7 to x/5 are stolen or something like that, and to remain displayed artifacts as constant the disappearance should happen from storage only.

Assuming worst case scenario that x/5 things were stolen. => 2x/3-x/5 = 7x/3
Now total artifacts are x/3+7x/3 = 8x/3
Storage is 7x/3
So Storage fraction will be 7/8 (Ans)

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by CSASHISHPANDAY » Wed Sep 19, 2012 10:45 pm
Answer Choices are

6/7, 13/20, 5/7, 11/18, 5/12
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by anuprajan5 » Wed Sep 19, 2012 10:55 pm
The answer is [spoiler]11/18[/spoiler]
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by KapilKapoor » Wed Sep 19, 2012 11:02 pm
There was a calculation error in the below, the same is bolded.
Hi,

Assume the museum has x artifacts.

x/3 = display
2x/3 = storage

x/7 to x/5 are stolen or something like that, and to remain displayed artifacts as constant the disappearance should happen from storage only.

Assuming worst case scenario that x/5 things were stolen. => 2x/3-x/5 = 7x/15
Now total artifacts are x/3+7x/15 = 12x/15
Storage is 7x/15
So Storage fraction will be 7/12 (Ans)
If choices don't match, as i was expecting then we must consider => 2x/3-x/7 = 11x/21

Now total artifacts are x/3+11x/21 = 18x/21
Storage is 11x/21
So Storage fraction will be 11/18

Now we have two options => 7/12 & 11/18, The actual answer will lie between these two including both.

Ans = d

Thanks & Regards,
Kapil
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by Ian Stewart » Wed Sep 19, 2012 11:06 pm
We're keeping the same number of artifacts on display as before, so we might as well just assume that all of the stolen artifacts were stolen from storage. We want to keep as many things in storage as possible, so we want the number of stolen artifacts to be as small as possible, and we should assume 1/7 of all artifacts were stolen. Since this is a pure ratio question, we can now just pick a number. Say we had 21 artifacts in total to begin with. Then 7 artifacts were on display to begin with. After 1/7 of the artifacts are stolen, we have 18 left, and we still want to display 7 of them, so 11/18 of the artifacts remain in storage.
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