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# In the triangle above, does a^2 + b^2 = c^2 ?

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Math Expert
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In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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03 Jan 2014, 05:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Untitled.png [ 11.7 KiB | Viewed 9793 times ]
In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y = 90
(2) x = y

Data Sufficiency
Question: 19
Category: Geometry Triangles
Page: 154
Difficulty: 600

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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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03 Jan 2014, 05:20
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SOLUTION

In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y = 90. This implies that the third angle, which is opposite side c, is 90 degrees. Thus a^2 + b^2 = c^2. Sufficient.

(2) x = y. This implies that the triangle is isosceles. If it's an isosceles right triangle, then the answer is YES but if it's not, then the answer is NO. Not sufficient.

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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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03 Jan 2014, 06:02
2
IMO: A

1) x + y= 90
Therefore, the other angle equals 90°, the triangle is a right triangle, and the formula is a^2 + b^2 = c^2
SUFFICIENT

2) x = y.
x + y = 90°, therefore, the triangle is a right triangle.
x + y = 88°, therefore, it is not a right triangle. (Be careful, do not assume anything based on the figure).

Hence A
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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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03 Jan 2014, 10:39
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y= 90
(2) x = y

Data Sufficiency
Question: 19
Category: Geometry Triangles
Page: 154
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Statement A:

if x+y=90. that means other side will be 90. this wud be right angle.

I think this is sufficient. A.

Statement B : x=y that means other side can be any number.

x=40 and y=40 other side cud be 100. so its not sure it cud be a2+b2=c2 or not.

so b is not sufficient.

Hence ans is a.
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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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05 Jan 2014, 10:29
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y= 90
(2) x = y

Statement 1) If x+y = 90 then the angle opposite of Side c has to have angle of 180-90 = 90, and the sides will satisfy the pythagorus theorem. Sufficient.
Statement 2) x = y. it is just a condition of isosceles triangle. Not Sufficient.

hence Option A)
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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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05 Jan 2014, 11:19
SOLUTION

In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y = 90. This implies that the third angle, which is opposite side c, is 90 degrees. Thus a^2 + b^2 = c^2. Sufficient.

(2) x = y. This implies that the triangle is isosceles. If it's an isosceles right triangle then the answer is YES but if it's not, then the answer is NO. Not sufficient.

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Re: In the triangle above, does a^2 + b^2 = c^2 ?  [#permalink]

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10 Jun 2018, 10:04
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the triangle above, does a^2 + b^2 = c^2 ?

(1) x + y = 90
(2) x = y

Target question: Does a² + b² = c²?
This is a good candidate for rephrasing the target question.
a² + b² = c² should look familiar - it's the Pythagorean Theorem
In order for a² + b² = c², the triangle MUST be a RIGHT TRIANGLE
So, we can REPHRASE the target question....
REPHRASED target question: Is the triangle a right triangle?

NOTE: We can rephrase this version even more if we recognize that in the Pythagorean Theorem (a² + b² = c²), c represents the length of the hypotenuse.
So, in order for the Pythagorean Theorem to hold true in this example, the angle opposite side c must be a right angle.
So, we can RE-REPHRASE the target question as....
RE-REPHRASED target question: Is the angle opposite side c a right angle?

Now onto the statements!!!

Statement 1: x + y = 90
Since all 3 angles in a triangle must add to 180°, the missing angle must equal 90°.
In other words, the angle opposite side c IS a right angle
Since we can answer the RE-REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 45° and y = 45°. This means the 3rd angle (the angle opposite side c) = 90°. In this case, the answer to the RE-REPHRASED target question is YES, the angle opposite side c IS a right angle
Case b: x = 40° and y = 40°. This means the 3rd angle (the angle opposite side c) = 100°. In this case, the answer to the RE-REPHRASED target question is NO, the angle opposite side c is NOT a right angle
Since we cannot answer the RE-REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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Re: In the triangle above, does a^2 + b^2 = c^2 ?   [#permalink] 10 Jun 2018, 10:04
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