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# Q. A cash register in a certain clothing store is the same

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Manager
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Q. A cash register in a certain clothing store is the same [#permalink]  21 Feb 2007, 20:39
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Q. 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
Intern
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sgoll I'd say the shortest distance would be if the register lied in the line that joins the dressing rooms, so that would be 8 feet from each room. Down to BCE. I can't come up with a reason why II and III cannot be so I would have put E as the answer.
Director
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You should draw a triangle on this one...

We know the base: that is the distance between two dressing rooms.
And we know that the other two sides of the triangular must be equal, thus isosceles tringle: that is the distance to the cashier...

Then apply the triangular rule and pick E....

I) cannot be because the sum of those two sides would equal 12, which is less than 16 and cannot be true...

II) is Ok
III) is Ok.
Manager
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So crrrrg and SimaQ, both of you mean to say we need to apply simply the triangular rule and no other calculation is required?
Intern
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sgoll I don't know what the triangular rule is but yes it helped me draw a straight line joining all 3 points and then the triangle as SimaQ suggested. I don't think any other calculation is necessary. If the register is equidistant from both dressing rooms and they are separated by 16 feet then the minimum distance from either is 8 feet, anything less than that can't be.
Director
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crrrrg wrote:
sgoll I don't know what the triangular rule is but yes it helped me draw a straight line joining all 3 points and then the triangle as SimaQ suggested. I don't think any other calculation is necessary. If the register is equidistant from both dressing rooms and they are separated by 16 feet then the minimum distance from either is 8 feet, anything less than that can't be.

By triangular rule i mean that the sum of any two sides of the triangle cannot be less or equal the length of the the remaining side.

However, 8 is also a possibility in this example as the point of cashier can be drawn on the straight line along with two dressing rooms. Thus, in this case obviously, triangular rule does not apply....
What i want to stress that if there was an option with figure 8, you should choose it as a correct answer also... All other options, would definetely have to be considered using the triangular rule as there would be no way to put the point that would be equidistant from the other two points....
Intern
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Thanks for the explanation SimaQ, you explained it well and good that we agree on E. The triangular rule was what I was thinking about just didn't call it that.
Manager
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The explanations make sense to me. Thanks crrrrg and SimaQ
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Re: Unanswered PS Ques- Distance between dressing rooms [#permalink]  17 Mar 2008, 08:20
i dont think this question has anything to do with the triangle rule
its more of a coordinate geometry question.

think of d1 and d2 as a flat line 16 units long.
if r is equidistant from d1 and d2, the shortest distance from r to d1 would be if r is placed as a midpoint.
Thus the shortest distance is 8.
There are an inifinite number of equdistant points between d1 and d2.
Essentially, any number from 8 or higher can be the distance.

This is the concept:
http://regentsprep.org/REgents/math/loc ... cusPTS.htm
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Re: Unanswered PS Ques- Distance between dressing rooms   [#permalink] 17 Mar 2008, 08:20
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