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

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Untitled.png [ 11.7 KiB | Viewed 5734 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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[Reveal] Spoiler: OA

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

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03 Jan 2014, 06:20
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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, 07:02
2
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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, 11:39
1
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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:
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, 11:29
1
KUDOS
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, 12:19
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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03 Oct 2015, 12:03
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Re: In the triangle above, does a^2 + b^2 = c^2 ? [#permalink]

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08 Jan 2017, 03:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the triangle above, does a^2 + b^2 = c^2 ?   [#permalink] 08 Jan 2017, 03:30
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# In the triangle above, does a^2 + b^2 = c^2 ?

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