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In right triangle ABC, x = ?

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by AAPL » Fri Dec 15, 2017 4:00 pm
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In right triangle ABC, x = ?

A. 6
B. 8
C. 6√2
D. 10
E. 13

The OA is A.

Experts, in this PS question I just need to solve the following equation,

$$x^2+\left(x+2\right)^2=\left(2x-2\right)^2$$

right? (Pitagoras's theorem) Thanks!
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by Brent@GMATPrepNow » Fri Dec 15, 2017 4:22 pm
AAPL wrote: Experts, in this PS question I just need to solve the following equation,

$$x^2+\left(x+2\right)^2=\left(2x-2\right)^2$$

right? (Pitagoras's theorem) Thanks!
Exactly!!

Cheers,
Brent
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by GMATWisdom » Sat Dec 16, 2017 8:54 am
AAPL wrote:Image

In right triangle ABC, x = ?

A. 6
B. 8
C. 6√2
D. 10
E. 13

The OA is A.

Experts, in this PS question I just need to solve the following equation,

$$x^2+\left(x+2\right)^2=\left(2x-2\right)^2$$

Applying Pythagorus theorem and finding the value of x is absolutely OK but its more time consuming than applying Pythagorus theorem and plugging in options. You yourself may try and see option A is correct without much effort.

right? (Pitagoras's theorem) Thanks!
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by [email protected] » Sat Dec 16, 2017 11:32 am
Hi AAPL,

GMAT questions are often based on patterns - and the answer choices sometimes provide 'clues' as to how you might answer the question. Learning to spot (and use) all of that information can help you to answer questions in a faster/easier fashion.

Here, we're dealing with a RIGHT triangle. Notice how the lengths of the two 'legs' differ by exactly 2. What's the first (fairly common) right triangle that you can think of that would fit THAT pattern. If nothing immediately comes to mind, then take a quick look at the five answer choices. One of those numbers IS the value of X... and would fit the pattern that we've already discussed. If you still don't see the pattern, then you should try TESTing THE ANSWERS (plug them in and see which one 'fits' all of the given information.

As a hint for this prompt, one of the most common right triangles that the GMAT builds Geometry questions around is the 3/4/5. Knowing that, how quickly can you answer this question now?

Final Answer: A

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Rich
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