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What is the area of right triangle XYZ?

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What is the area of right triangle XYZ? [#permalink]

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New post 29 Dec 2014, 21:47
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What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.
(2) Side XZ is 15 inches long.
[Reveal] Spoiler: OA

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What is the area of right triangle XYZ? [#permalink]

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Hi there,

I found this question really tricky.

You can see that if the right answer is E, the reasoning obviously implies that even combining both statements you don´t have sufficient information to answer the question. As for this problem, this means that:
- EITHER XZ is the hypotenuse and therefore XY is 12 (the magic Pythagorean triple we all learnt!)
- OR XZ is not the hypotenuse and therefore XY is actually the hypotenuse. This would be written as 9^2 + 15^2 = XY^2. Therefore, XY = \(\sqrt{306}\) = 17.5 approx.

Both options yield to different areas for the triangle. Hence, E.

My confusion is the following:
If the question stem states that we have a right triangle XYZ, doesn´t that imply that Y = 90º (the central letter = 90º)? In other words, doesn´t that imply that YZ and YX MUST BE the legs?
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Re: What is the area of right triangle XYZ? [#permalink]

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When the GMAT is describing a right triangle using the names of the vertices (ABC, XYZ, etc.), there is no convention on where the right angle is, so it could be at vertex A, B or C.

However, when the GMAT is describing angles by using the adjacent vertices, then the middle letter is the vertex where the angle is located. E.g. angle ABC is the angle inscribed by the vertices A, B and C.
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Re: What is the area of right triangle XYZ? [#permalink]

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New post 30 Dec 2014, 10:57
littlewarthog wrote:
When the GMAT is describing a right triangle using the names of the vertices (ABC, XYZ, etc.), there is no convention on where the right angle is, so it could be at vertex A, B or C.

However, when the GMAT is describing angles by using the adjacent vertices, then the middle letter is the vertex where the angle is located. E.g. angle ABC is the angle inscribed by the vertices A, B and C.

Thanks for the explanation!
+1 for you
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Re: What is the area of right triangle XYZ? [#permalink]

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New post 14 Oct 2015, 10:47
Can we also think of it like, they said it was a right angle triangle, but we don't know if it's a 30-60-90 or a 45-45-90 triangle. Would that also be a factor we can consider in this question?
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What is the area of right triangle XYZ? [#permalink]

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minwoswoh wrote:
What is the area of right triangle XYZ?

(1) Side YZ is 9 inches long.
(2) Side XZ is 15 inches long.


Target question: What is the area of right triangle XYZ?

KEY CONCEPT: Area of triangle = (1/2)(base)(height)
So, to answer the target question, we need lengths of BOTH the base AND the height.

Statement 1: Side YZ is 9 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Side XZ is 15 inches long.
We have only 1 measurement. So, there's no way to determine the area of the triangle.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We still don't have enough information.
Consider the following 2 cases (which both satisfy the given conditions).

case a:
Image
Here, the area = (1/2)(9)(12) = 54

case b:
Image
Here, the area = (1/2)(9)(15)= 67.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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Originally posted by GMATPrepNow on 14 Oct 2015, 12:27.
Last edited by GMATPrepNow on 16 Apr 2018, 13:01, edited 1 time in total.
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Re: What is the area of right triangle XYZ? [#permalink]

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Re: What is the area of right triangle XYZ?   [#permalink] 17 Dec 2017, 01:44
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