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random DS geometry

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random DS geometry

by xcise_science » Mon Nov 19, 2007 10:07 am
Image

Can someone tell me if I 'over-assumed' or arrived at the answer incorrectly?

Here's how I looked at this question:
-D is where B meets PR
-I know there's a rule that triangles inscribed in a semi-circle are right triangles. So I concluded that PQR is a right triangle (angle Q is 90)
-Then I reasoned that line B bisects angle Q and splits it into equal angles (I think bisecting lines splits angles in half); therefore angle PQD is 45, and the triangle is 45-45-90.
So all I need to determine B is a value for any of the legs of that triangle.
stmt 1: not sufficient
stmt 2: tells me hypotenuse is sq. root of 84. sufficient.

This is the right answer, but I'm trying to see if I assumed incorrectly, but still somehow ended up with the right answer.

Also, I heard that either in PS or DS questions (not sure which), when you are giving a number, it is usually for a reason. Because I see that I didn't use the value given (5) in this question.

Thanks
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by samirpandeyit62 » Mon Nov 19, 2007 9:11 pm
First of all I must say this problem is a little difficult

now getting to the pt

angle PQD cannot be 45 as QD does not bisect PR, if it did then stmt 1 was suff itself coz both the triangles would be 45-45-90 & congruent which is not possible here.

stmt 1: INSUFF

stmt 2:

PQ = rt(84)

now b^2 = 84 - PD^2 -------1

also b^2 = c^2 -25

& c^2 = (PD + 5) ^2 - 84

so b^2 = PD^2 + 10PD +25 - 25 -84

b^2 =PD^2 + 10PD -84 --------2

so from 1 & 2

PD^2 + 10PD -84 = 84 - PD^2

2PD^2 +10PD -168 = 0

PD^2 + 5PD -84 =0

so PD = -12 or PD =7

it cannot be -ve so PD = 7

so b = rt (35)

B

hey xcise BTW where did u encounter this prob.
Regards
Samir
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by xcise_science » Tue Nov 20, 2007 10:07 am
WOW! I had to rewrite your explanation and it took me about 5minutes.
Ok, I think I should just settle for a 570 :(

But thanks anyway.
The question was from my GMAT prep class from a program called Bellcurves (in NYC).
Though their questions are ridiculously hard, I don't mind that. I just don't like/understand some of their explanations.

For instance, for this question, here's what they wrote (in bold):
Rephrase: We are looking for b and have another leg in the right triangle already. We can determine the length of b using the Pythagoream Theorem if we find the length of c.
(They are referring to triangle QDR, right? So knowing C, you can figure out B)

Statements
(1) This statement gives us information on a different length, BC, that isn't part of the triangle.
Insufficient. Eliminate A and D.
(2) This statement gives us a value for length PQ, which is what we are looking for in our rephrase, the value for another length in the triangle.
Sufficient Choose B:
My question is, how does knowing PQ help you to determine a leg in QDR (or PDQ)? Since both have the same height.
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