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Triangle QRS is inscribed in a circle as shown above....

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Triangle QRS is inscribed in a circle as shown above....

by cherry yeung » Wed Dec 28, 2016 7:14 am
Hi,

Could some please help to explain why statement 2 cannot be used to confirm qrs is a right of triangle? Based on Pythagorean theorem, if qrs is a right angle triangle, qr's square root + qs's square root = rs's square root. Thus qs = 4. Which is a right angle triangle.

Please see attached picture for question and explanation from the book.

Regards,

Cherry
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Dec 28, 2016 7:27 am
cherry yeung wrote:Hi,

Could some please help to explain why statement 2 cannot be used to confirm qrs is a right of triangle? Based on Pythagorean theorem, if qrs is a right angle triangle, qr's square root + qs's square root = rs's square root. Thus qs = 4. Which is a right angle triangle.

Please see attached picture for question and explanation from the book.

Regards,

Cherry
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The problem with your analysis of statement 2 is that you first assume that QRS is a right angle triangle so that you can use the Pythagorean theorem to find the length of the 3rd side. Once you find the length of the 3rd side, you conclude that QRS is a right angle triangle.

So, you are assuming that QRS is a right angle triangle in order to prove that QRS is a right angle triangle.

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Brent
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by [email protected] » Wed Dec 28, 2016 6:34 pm
Hi cherry yeung,

In DS questions, you can't trust that any pictures are drawn to scale (so you should be cynical about what you THINK a shape represents). Here, it looks the triangle might be a right triangle, but there is no information to confirm that.

One of the ways to have a right triangle under those conditions is IF all three points are on the circumference of the circle AND one of the sides is the DIAMETER of the circle. Here, we don't know whether RS is the diameter or not, so there's no way to know whether we have a right triangle or not.

From Fact 2, we know that two of the sides are 3 and 5, so the missing side COULD be a 4 (which would be a right triangle), but it could also be 4.1 (which is NOT a right triangle).

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