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555-605 Level|   Geometry|   Word Problems|                     
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jabhatta2
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Jack wants to use a circular rug on his rectangular office floor to co 04 Jan 2023, 10:45
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danpo
To follow up on some people's comment that the >3 feet distance from the nearest wall is redundant information: No, it's not.

As others have pointed out above, we can conclude from the combined statements (1) and (2) that the rug is large enough to cover both stains. However, the question is if the rug can be placed to cover both stains and to answer this, we must know that it's farther away from the wall than its radius. That is exactly why the 3 feet minimum distance is included in the question.

If the minimum distance was anything less than 3 feet, then the answer would actually be E.
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I am afraid I don't agree with the Yellow highlight above.

If the minimum distance was equal to 3 feet or less than 3 feet -- the answer to the question WOULD STILL BE "Yes".

Thus, I believe the statement "each more than 3 feet from the nearest wall" is frankly irrelevant.

Lets say, the minimum distance was LESS THAN 3 FEET -- the answer to the question stem would still be "Yes"

The rug can still be PLACED to cover both stains. Perhaps the rug has to be folded by half or perhaps some part of the Rug will be on the walls of the rectangular office, but the answer to the question would still be "Yes"

Placed = can include being placed flat, being placed half folded, being placed such that some bit of the rug is on the walls of the rectangular office.

avigutman zhanbo MartyTargetTestPrep

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Jack wants to use a circular rug on his rectangular office floor to co 04 Jan 2023, 10:59
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jabhatta2
danpo
To follow up on some people's comment that the >3 feet distance from the nearest wall is redundant information: No, it's not.

As others have pointed out above, we can conclude from the combined statements (1) and (2) that the rug is large enough to cover both stains. However, the question is if the rug can be placed to cover both stains and to answer this, we must know that it's farther away from the wall than its radius. That is exactly why the 3 feet minimum distance is included in the question.

If the minimum distance was anything less than 3 feet, then the answer would actually be E.


I am afraid I don't agree with the Yellow highlight above.

If the minimum distance was equal to 3 feet or less than 3 feet -- the answer to the question WOULD STILL BE "Yes".

Thus, I believe the statement "each more than 3 feet from the nearest wall" is frankly irrelevant.

Lets say, the minimum distance was LESS THAN 3 FEET -- the answer to the question stem would still be "Yes"

The rug can still be PLACED to cover both stains. Perhaps the rug has to be folded by half or perhaps some part of the Rug will be on the walls of the rectangular office, but the answer to the question would still be "Yes"

Placed = can include being placed flat, being placed half folded, being placed such that some bit of the rug is on the walls of the rectangular office.

avigutman zhanbo MartyTargetTestPrep

Thoughts ?
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Notice that the question says the following:

Jack wants to use a circular rug on his rectangular office floor

So, the rug is meant to be "circular" and "on his rectangular office floor."

Given that information, test-takers could reasonably presume that the entire rug is on the floor, as opposed to partly on a wall, and that it's used properly, as in flat on the floor in a circular shape. After all, we're talking about COVERING STAINS IN AN OFFICE. Covering stains by putting a folded rug on the floor of an office or having a rug partly on the wall would be pointless. Jack might as well leave the stains uncovered.

At the same time, what you're saying is still possible. Maybe the rug could be folded. So, to put all such questions to rest, the information that the stains are more than three feet from the walls is included.
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Jack wants to use a circular rug on his rectangular office floor to co 04 Jan 2023, 11:18
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MartyTargetTestPrep
Notice that the question says the following:

Jack wants to use a circular rug on his rectangular office floor

So, the rug is meant to be "circular" and "on his rectangular office floor."

Given that information, test-takers could reasonably presume that the entire rug is on the floor, as opposed to partly on a wall, and that it's used properly, as in flat on the floor in a circular shape. After all, we're talking about COVERING STAINS IN AN OFFICE. Covering stains by putting a folded rug on the floor of an office or having a rug partly on the wall would be pointless. Jack might as well leave the stains uncovered.

At the same time, what you're saying is still possible. Maybe the rug could be folded. So, to put all such questions to rest, the information that the stains are more than three feet from the walls is included.
Show more

Thank you so much MartyTargetTestPrep

Just wondering - if the phrase "each more than 3 feet from the nearest wall" was NOT given, would the answer REALLY BE (e) in your view ?

Danpo mentioned that in his post above (in the yellow highlight above)

I don't think the answer would be changed to (E), even if the phrase in the purple was NOT GIVEN.

-----------------------------------

The only way the answer would be (E) is if (S2) said this instead

(S2-variant ) The centers of the stains are less more than 4 feet apart
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Jack wants to use a circular rug on his rectangular office floor to co 04 Jan 2023, 11:41
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jabhatta2
MartyTargetTestPrep
Notice that the question says the following:

Jack wants to use a circular rug on his rectangular office floor

So, the rug is meant to be "circular" and "on his rectangular office floor."

Given that information, test-takers could reasonably presume that the entire rug is on the floor, as opposed to partly on a wall, and that it's used properly, as in flat on the floor in a circular shape. After all, we're talking about COVERING STAINS IN AN OFFICE. Covering stains by putting a folded rug on the floor of an office or having a rug partly on the wall would be pointless. Jack might as well leave the stains uncovered.

At the same time, what you're saying is still possible. Maybe the rug could be folded. So, to put all such questions to rest, the information that the stains are more than three feet from the walls is included.

Thank you so much MartyTargetTestPrep

Just wondering - if the phrase "each more than 3 feet from the nearest wall" was NOT given, would the answer REALLY BE (e) in your view ?

Danpo mentioned that in his post above (in the yellow highlight above)

I don't think the answer would be changed to (E), even if the phrase in the purple was NOT GIVEN.

-----------------------------------

The only way the answer would be (E) is if (S2) said this instead

(S2-variant ) The centers of the stains are less more than 4 feet apart
Show more
I think we could argue that the answer would be (E) without the information that each stain is more than three feet from the nearest wall since it's reasonable to presume that the idea is that the rug would be flat on the floor.
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Jack wants to use a circular rug on his rectangular office floor to co 29 Jan 2023, 05:56
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avigutman what would happen if >3ft case wasnt given?
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Jack wants to use a circular rug on his rectangular office floor to co 30 Jan 2023, 00:14
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jabhatta2
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Notice that the question says the following:

Jack wants to use a circular rug on his rectangular office floor

So, the rug is meant to be "circular" and "on his rectangular office floor."

Given that information, test-takers could reasonably presume that the entire rug is on the floor, as opposed to partly on a wall, and that it's used properly, as in flat on the floor in a circular shape. After all, we're talking about COVERING STAINS IN AN OFFICE. Covering stains by putting a folded rug on the floor of an office or having a rug partly on the wall would be pointless. Jack might as well leave the stains uncovered.

At the same time, what you're saying is still possible. Maybe the rug could be folded. So, to put all such questions to rest, the information that the stains are more than three feet from the walls is included.

Thank you so much MartyTargetTestPrep

Just wondering - if the phrase "each more than 3 feet from the nearest wall" was NOT given, would the answer REALLY BE (e) in your view ?

Danpo mentioned that in his post above (in the yellow highlight above)

I don't think the answer would be changed to (E), even if the phrase in the purple was NOT GIVEN.

-----------------------------------

The only way the answer would be (E) is if (S2) said this instead

(S2-variant ) The centers of the stains are less more than 4 feet apart
I think we could argue that the answer would be (E) without the information that each stain is more than three feet from the nearest wall since it's reasonable to presume that the idea is that the rug would be flat on the floor.
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MartyTargetTestPrep, Is rug folding considered as an option if asked this in Official?
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Jack wants to use a circular rug on his rectangular office floor to co 30 Jan 2023, 07:10
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MartyTargetTestPrep
Notice that the question says the following:

Jack wants to use a circular rug on his rectangular office floor

So, the rug is meant to be "circular" and "on his rectangular office floor."

Given that information, test-takers could reasonably presume that the entire rug is on the floor, as opposed to partly on a wall, and that it's used properly, as in flat on the floor in a circular shape. After all, we're talking about COVERING STAINS IN AN OFFICE. Covering stains by putting a folded rug on the floor of an office or having a rug partly on the wall would be pointless. Jack might as well leave the stains uncovered.

At the same time, what you're saying is still possible. Maybe the rug could be folded. So, to put all such questions to rest, the information that the stains are more than three feet from the walls is included.
MartyTargetTestPrep, Is rug folding considered as an option if asked this in Official?
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I doubt it. Such a question is about the properties of geometric shapes in two dimensions. This isn't a Google interview question such that we're expected to come up with an out-of-the-box answer that involves folding the rug or something else like that.
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Jack wants to use a circular rug on his rectangular office floor to co 08 Feb 2023, 23:52
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Elite097
avigutman what would happen if >3ft case wasnt given?
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Hello Elite097

This doubt has been talked about by other experts as well. Still, for your query I will respond here along with an image to help you visualize better.



The image above is a representation of the rectangular room, the small circular stain (drawn in brown), and the circular rug.

You see that if the circular spot was too close to the corner, the rug with its current dimensions would no longer be able to cover it. The edges of the rug are already touching the walls of the room.

We can safely assume that the rug would be placed flat on the floor and the rug would not be folded. Without folding the rug, we cannot push the rug more towards the corner and thus, the rug CANNOT cover the stain in this case.

Therefore, the condition that the stains are “more than 3 feet from the nearest wall” is a necessary condition. It cancels out the case where the stains are in the corner where the rug does not reach.

Without this information, the answer to this DS question would be E.


Hope it helps!

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Jack wants to use a circular rug on his rectangular office floor to co 01 Oct 2024, 15:24
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