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interesting question on pythagaurean triplet

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interesting question on pythagaurean triplet

by ritz » Tue Apr 08, 2008 3:13 pm
If in the attached question, we had 13 as the diameter of the circle, should we choose B as the answer.
Why i am asking this is because I know that there is a pythagaurean triplet 13 12 & 5.
So I would know the other 2 sides & can find the area of the triangle.
any comments please as i think it is a very smart question & i think GMAT might throw something like this.
should we use the knowledge of pythagaurean triplets in gmat?

thanks
RItz
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by Stuart@KaplanGMAT » Tue Apr 08, 2008 4:38 pm
A very common mistake that I've seen on these boards is people assuming that knowing 1 side of a right angle triangle is enough to determine the other 2 sides. This assumption is 100% incorrect.

Let's look at your suggestion: if we know that d=13 we know that the other sides are 5 and 12.

If we plug into the theorem, we'd get:

a^2 + b^2 = 169.

Are the only possible values of a and b 5 and 12? Of course not. We have one equation and 2 unknowns, there are infinite possible values for both a and b. For example:

a = root167, b = root2
a = root100, b = root69
a = root18.5, b = root 150.5

So, just knowing that the diameter is 13 (and that the hypotenuse is the diameter of the circle) would NOT be sufficient, since we need the base and the height (i.e. a and b) to calculate the area of the triangle.

In this particular question, we don't even know that the hypotenuse is the diameter of the circle, so the triangle doesn't even have to be right. Even combined, it could be a 30/30/120 or 30/40/110 or an infinite number of other triangles. Hence, the answer is (e), not enough information.

Actually, let me go one step further:

a chord of the circle = 18
the circumference = 18

Well, circumference = pi(d)
so, pi(d) = 18
d = 18/pi which is < 18

Umm.. the diameter of a circle is the biggest possible chord. How can we have a chord that's bigger than the diameter? We can't! No clue where this question is from, but you would NEVER see it on the real GMAT, because it draws an impossible shape.
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by ritz » Tue Apr 08, 2008 7:22 pm
thanks Stuart.

my assumption was that we should consider triplets knowledge when we solve the DS question & you solved that doubt.
As far as the question is concerned, the question talks about the length as 18 only. I gave the example of 13 becuase it has a triplet & 18 does not have...
anyways, i got the clarification & i thank you for that..
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by mmukher » Wed Apr 09, 2008 5:11 am
I suppose if a and b are integers then you could assume the 5,12,13 triplet thing.

For the question at hand, like Stuart mentioned, there is not enough information available to solve it.

Oh by the by, Im in CT. (test on the 19th at 8am). One more weekend to go!

-- Mayukh
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