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A cash register in a certain clothing store is the same

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A cash register in a certain clothing store is the same [#permalink] New post 12 Oct 2005, 12:57
A cash register in a certain clothing store is the same distance from two dressing rooms in the store. If the distance between the two dressing rooms is 16 feet, which of the following could be the distance between the cash register and either dressing room?
I. 6 feet
II. 12 feet
III. 24 feet
A. I only
B. II only
C. III only
D. I and II
E. II and III
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 [#permalink] New post 12 Oct 2005, 13:21
If you have a triangular arrangement...

difference of two sides < length of third side < sum of two sides

(1) 10 < l < 22, l=6 so this cannot be a sol'n

(2) 4 < l < 28, l = 12 this can be a sol'n

(3) 8 < l < 40, l = 24 this can be a sol'n

answer is E?
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 [#permalink] New post 12 Oct 2005, 13:32
To clarify further the question states, the distance from cashier and dressing rooms are equal. So the arrangement would be isosceles triangle.

We can work through the choices and applying the formula we get the answer (E)
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 [#permalink] New post 12 Oct 2005, 21:43
The cash register lies on the line that is the perpendicular bisector of the line connecting the two rooms. So the cash register is always >= 8feet from either of the rooms.
Ans E
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 [#permalink] New post 12 Oct 2005, 21:52
A case of an isosceles triangle. E it is.
_________________

Cheers, Rahul.

  [#permalink] 12 Oct 2005, 21:52
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