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

Question

https://gmatclub.com/forum/download/file.php?id=21922 In the triangle above, does a^2 + b^2 = c^2 ? (1) x + y = 90 (2) x = y Untitled.png

Bunuel · Answer

SOLUTION

https://gmatclub.com/forum/download/file.php?id=21922 
 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.

ugo2602 · Answer

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

sanjoo · Answer

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.

kinjiGC · Answer

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)

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine whether a^2 + b^2 = c^2. That is, we need to determine whether the triangle is a right triangle.

Statement One Alone:

Since x + y = 90, the unlabeled angle must be 180 - 90 = 90 degrees. In other words, it’s a right angle, and so the triangle is a right triangle. Therefore, we do have a^2 + b^2 = c^2. Statement one alone is sufficient.

Statement Two Alone:

Statement two is not sufficient. For example, if x = y = 45, then the triangle is a right triangle. However, if x = y ≠ 45, then the triangle is not a right triangle.

Answer: A

bumpbot · Answer

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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 ?

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