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by pakaskwa » Fri Mar 06, 2009 4:17 am
First of all, for any right triangle with 3 vertices at 30, 60 and 90 degrees, the ratio of its all sides is 1:sqrt3:2 (with 2 as its hypotenuse). This is worth to memorize.

Using OP and OQ as 2 hypotenuses, we can make 2 right triangles with axis x and y. And they are congruent. Length of each side is 1, sqrt3, 2. All vertices are 30, 60, and 90.

Therefore, for point Q(s,t), s=1, t=sqrt3.

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by Brent@GMATPrepNow » Fri Mar 06, 2009 10:59 am
Here's a visual version of the solution:

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by Vemuri » Mon Mar 09, 2009 11:56 pm
Wow !!! That was an eye opening explanation. Thanks a ton Brent !!!

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by avenus » Sat Mar 14, 2009 3:42 am
One question:

I had understood that on the real GMAT PS (not DS) figures are drawn to scale unless explicitly stated otherwise. This is clearly not the case here.

Is that assumption wrong or is this a (partly) defective question?

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by Ian Stewart » Sat Mar 14, 2009 7:13 am
avenus wrote:One question:

I had understood that on the real GMAT PS (not DS) figures are drawn to scale unless explicitly stated otherwise. This is clearly not the case here.

Is that assumption wrong or is this a (partly) defective question?
Given how many prep books say that diagrams are always to scale on the GMAT unless stated otherwise, I imagine that was true at some point in the history of the test. As the question above illustrates, it's not true any more. If you want to estimate something from a diagram, be sure to draw the diagram yourself based on available information.
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by avenus » Sun Mar 15, 2009 2:25 am
Given how many prep books say that diagrams are always to scale on the GMAT unless stated otherwise, I imagine that was true at some point in the history of the test. As the question above illustrates, it's not true any more. If you want to estimate something from a diagram, be sure to draw the diagram yourself based on available information.
Ian, thanks for your reply.

The OGs (both the (orange) general and the Math review, last available editions) have a piece of text before the PS sections (not the DS ones) stating, I quote:

"A figure accompanying a PS question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may appear jagged. All figures lie in a plane unless otherwise indicated"

They clearly say that these directions are very similar to those encountered at the real test. They even advise people to read the instructions carefully and understand them clearly before sitting the real GMAT so that you don't have to spend too much time reading them on test day.

This is consistent with the info I've come across in pretty much every prep book I've worked with so far.

Assuming this is not true would actually imply the OG is putting out somewhat misleading information. I can't imagine that's the case.

Any thoughts?

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by Ian Stewart » Sun Mar 15, 2009 3:02 am
avenus wrote: The OGs (both the (orange) general and the Math review, last available editions) have a piece of text before the PS sections (not the DS ones) stating, I quote:

"A figure accompanying a PS question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may appear jagged. All figures lie in a plane unless otherwise indicated"

They clearly say that these directions are very similar to those encountered at the real test. They even advise people to read the instructions carefully and understand them clearly before sitting the real GMAT so that you don't have to spend too much time reading them on test day.

This is consistent with the info I've come across in pretty much every prep book I've worked with so far.

Assuming this is not true would actually imply the OG is putting out somewhat misleading information. I can't imagine that's the case.

Any thoughts?
The 11th edition of the OG is almost four years old now, and it predates the change in test developer from ETS to ACT, so some of the information it contains will be out of date. It's better to trust more recent materials (at least until OG12 is out), and the instruction screens in GMATPrep should be essentially just like the real thing. I'd be interested to know what they say about diagrams (I'd check myself, but I only have Macs at home, so can't run the software here) - it's been a while since I've read the instruction screens in any detail.

Regardless of what the instructions say, however, the question in the original post above clearly illustrates that diagrams in GMAT questions are not always drawn to scale, and I would always trust what logic and mathematical reasoning tell me, rather than what a picture provided with the question tells me. It's risky to put too much faith in a diagram - I've often seen students guess an angle is, say, 90 degrees only because it appears to be a right angle in the diagram, and those kinds of assumptions will normally land you in traps.
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