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Wrong answer in Princeton review?

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Wrong answer in Princeton review?

by hetavdave » Wed Jun 24, 2009 1:01 am
ABCD is a rectangle with sides of length x centimeter and width of y centimeter and a diagonal of length z centimeter. what is the measure, in centimeter , of the perimeter of rectangle ABCD.

1) x- y= 7
2) z =13

OA is C but i don't agree with that.

My understanding is -
on 5-12-13 pyathagoras rule,

Since ABCD is a rectangle, and z a diagonal of 13 centi, the length of sides (AB, BC) must be 5 and 12.

It doesn't matter to us which side is longest since we are interested in finding the perimeter.

Please let me know if i am wrong on this.
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by Morgoth » Wed Jun 24, 2009 4:18 am
I agree with you, the answer should B.

diagonal of a rectangle

z^2 = x^2 + y^2

this forms the hypotenuse equation

if z=13, z being the hypotenuse, x and y have to be 5 and 12.

Hence, we can easily find the perimeter.
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by david4431 » Wed Jun 24, 2009 5:00 am
Answer: C.

You cannot assume that the 2 triangles formed are 30-60-90 triangles.

What if it is a square with a diagonal of 13? Be careful with geometry questions that seem to imply 30-60-90. Each side could be sqrt (84.5). This would give you 9.1823... for each side. If you were to square each side, you would get 84.5; after adding the sides together, you will get 169. Take the square root of that sum and you are back at a diagonal of 13.
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by sanjib » Wed Jun 24, 2009 6:14 am
Hi Guys,
I think Dravid is right. However for Hetavdave let me try to focus his PithaG. theory little bit.
Guess we all focusing on Stm.2
it says the diagonal is 13.
as per Uncle sams(Pitah g.) theory:
L^2+W^2=HYP^2
L^2+W^2=13^2
L^2+4^2=13^2 (guessing it 4)
L^2= 169-16=145
L = @ 12. something
same way if we put any number less than 12 in place of L or W it would comeup with all kinds of value and all of them would follow the PithaG theory.
So we need to contact Stm 1 and thats why OA is C.
Feel free if you still have question on it.Because clarity bring score in GMAT
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by rajshree.misra » Wed Jun 24, 2009 7:44 am
Hi,

I completely agree with David. The second statement says that z = 13. Although 5/12/13 is a right angle triangle combination, it would be incorrect to assume that the two sides could be any other numbers whose squares add up to 169. Hence, the first statement is required to conclude that the right angle triangle combination is 5/12/13.

Hence the answer would be C.

Thanks,
N
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by Ian Stewart » Wed Jun 24, 2009 9:41 am
david4431 wrote:Answer: C.

You cannot assume that the 2 triangles formed are 30-60-90 triangles.
Note that hetavdave was not assuming the triangle was a 30-60-90 (the acute angles in the 5-12-13 right triangle are certainly not 30 and 60 degrees). Otherwise, I agree with your conclusion. I've noticed that, because so many prep books talk at length about 3-4-5 and 5-12-13 triangles, and about 30-60-90 and 45-45-90 triangles, that test takers often start seeing these triangles in questions when they aren't really there. Only conclude you are looking at one of these triangles when you have a perfectly logical reason to reach such a conclusion - e.g. if you know two of the three sides of a right triangle, or if you have used angles rules to prove you have the required angles. Otherwise you're likely making an unfounded assumption.

In the above question, we could very easily have a 1-root(168)-13 triangle, or we could have a 5-12-13 triangle using Statement 2 alone, so it is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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