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

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

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New post 03 Jan 2014, 06:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
Untitled.png [ 11.7 KiB | Viewed 6964 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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New post 03 Jan 2014, 06:20
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SOLUTION

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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.

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

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New post 03 Jan 2014, 07:02
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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New post 03 Jan 2014, 11:39
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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:
1. Please provide your solutions to the questions;
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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New post 05 Jan 2014, 11:29
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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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New post 05 Jan 2014, 12:19
SOLUTION

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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.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 10 Jun 2018, 11:04
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

Answer: A

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Re: In the triangle above, does a^2 + b^2 = c^2 ?   [#permalink] 10 Jun 2018, 11:04
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