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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.

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Re: In the triangle above, does a^2 + b^2 = c^2 ?
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03 Jan 2014, 06:20

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1

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, 07:02

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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).

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.

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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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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 ?
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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.

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