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Bunuel
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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Bunuel

In right triangle ABC, x =

A. 6
B. 8
C. \(6\sqrt{2}\)
D. 10
E. 13

Attachment:
ptr1q05.gif

If we didn't spot the approaches used by the above posters, we could also solve this question by TESTING the answer choices.
NOTE: this approach could be quite time-consuming!

A. x = 6
So, when we plug x = 6 into the 3 lengths, we see that the sides have lengths 6, 8 and 10
Now, we must check whether these 3 lengths could be legitimate lengths of a RIGHT TRIANGLE.
To be legit, they must satisfy the equation that applies to all right triangles: Pythagorean Theorem (a² + b² = c²).
Since 10 is the longest side, it would be the hypotenuse
So, now we check whether 6² + 8² = 10²
Evaluate: 36 + 64 = 100
It WORKS!

So, the answer is A.

Cheers,
Brent
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Hello,I solved this question by solving equations(pythagorean therorem),just wanted to ask what if first choice was not given as 6 and 6 was given at last.?will plugging method wont take much time?
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.




By Pythagorean theorem (2x-2)^2=x^2 + (x+2)^2
4x^2 -8x +4 = 2x^2 + 4x +4 ---> 2x^2 -12x =0 ---> 2x(x-6)=0.

So x=0 or 6. The answer is A.
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Hi vaidhaichaturvedi,

GMAT questions are often designed to give critical thinkers certain advantages. By paying attention to the answer choices, you can sometimes discover a pattern, hint or other shortcut to answering the question. Remember that NOTHING about GMAT questions is random - EVERYTHING is carefully designed (including the wrong answer choices). Thus, even if '6' was one of the larger answers, there would likely still be 'hints' that one of the regularly-tested triangles was involved in this question.

GMAT assassins aren't born, they're made,
Rich
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