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# In the figure above (attached), what is the length of PQ

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Manager
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In the figure above (attached), what is the length of PQ [#permalink]  03 Jan 2007, 20:00
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In the figure above (attached), what is the length of PQ times the length of RS?

1) The length of PQ is 5.
2) The length of QR times the length of PR is equal to 12.
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triangle_deleteme.JPG [ 3.41 KiB | Viewed 765 times ]

VP
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Re: Triangle DS [#permalink]  03 Jan 2007, 20:08
ellisje22 wrote:
In the figure above (attached), what is the length of PQ times the length of RS?

1) The length of PQ is 5.
2) The length of QR times the length of PR is equal to 12.

C

1) is INSUFF

2) QR may be 3/x and PR may be 4x So we cannot say anything about PQ

So taking both (1) and (2)

1/2*PR*QR = 1/2*RS*PQ
Manager
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Actually... [#permalink]  04 Jan 2007, 06:59
Actually the OA from Princeton Review is B. I personally thought it should have been D for the logic below:

Statement 1 should be sufficient because...
The question is basically looking for the area of the triangle.
You are given in statement 1 that PQ equals 5, so shouldn't you know that PS must be 2.5 and QS must be 2.5?
And since you know that triangle PRS is a 90-45-45 triangle (since you are given a 90 degree angle and you can see that the angle at R is split in half) than you have an isoceles triangle.
And since you know that PS is 2.5, then you'd know that RS is also 2.5 (since the sides opposite equal angles should be equal)?
Finally since you are given PQ and you figured out RS from the steps above, this statement should be sufficient.

Statement 2 is sufficient (which I agree with the book on) because...
The question is basically looking for the area of the triangle.
PR times QR should equal PQ times RS

Am I wrong or is the book wrong?
SVP
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Re: Actually... [#permalink]  04 Jan 2007, 07:09
ellisje22 wrote:
Actually the OA from Princeton Review is B. I personally thought it should have been D for the logic below:

Statement 1 should be sufficient because...
The question is basically looking for the area of the triangle.
You are given in statement 1 that PQ equals 5, so shouldn't you know that PS must be 2.5 and QS must be 2.5?
And since you know that triangle PRS is a 90-45-45 triangle (since you are given a 90 degree angle and you can see that the angle at R is split in half) than you have an isoceles triangle.
And since you know that PS is 2.5, then you'd know that RS is also 2.5 (since the sides opposite equal angles should be equal)?
Finally since you are given PQ and you figured out RS from the steps above, this statement should be sufficient.

Statement 2 is sufficient (which I agree with the book on) because...
The question is basically looking for the area of the triangle.
PR times QR should equal PQ times RS

Am I wrong or is the book wrong?

This is where the problem is. In GMAT test, we never can rely on the figure. The figure wrongly represents a kind of half of a square.

But, it is not. We cannot say that the 2 other angles are 45 degree each. So, we could have any kind of right triangular

The OA is correct
Senior Manager
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Re: Triangle DS [#permalink]  06 Jan 2007, 10:56
ellisje22 wrote:
In the figure above (attached), what is the length of PQ times the length of RS?

1) The length of PQ is 5.
2) The length of QR times the length of PR is equal to 12.

(1) We need RS to have sufficient data. As the angles at Q and P are not determined, RS is not determined => Insuff => B, C or E.

(2) PR * RS = 2 * Area of the triangle.
From the diagram: Area of the triangle = QR * PR = given data => PR * RS is determined => Suff => B.
Re: Triangle DS   [#permalink] 06 Jan 2007, 10:56
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