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Re: In the triangle above, does a^2 + b^2 = c^2 ?
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03 Jan 2014, 05:20
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Expert Reply
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.
Re: In the triangle above, does a^2 + b^2 = c^2 ?
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03 Jan 2014, 06:02
2
Kudos
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).
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. _________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
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.
Re: In the triangle above, does a^2 + b^2 = c^2 ?
[#permalink]
05 Jan 2014, 11:19
Expert Reply
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.
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
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.
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