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# In right triangle ABC, x =

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Math Expert
Joined: 02 Sep 2009
Posts: 48119
In right triangle ABC, x =  [#permalink]

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04 Dec 2015, 00:44
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5% (low)

Question Stats:

93% (01:18) correct 8% (02:04) wrong based on 80 sessions

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In right triangle ABC, x =

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

Attachment:

ptr1q05.gif [ 1.43 KiB | Viewed 1514 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 6565
Re: In right triangle ABC, x =  [#permalink]

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04 Dec 2015, 07:48
1
Bunuel wrote:

In right triangle ABC, x =

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

Attachment:
ptr1q05.gif

Hi,
we can do algebrically ..
sum of square of two legs =square of the hypotenuse..
x^2 + (x+2)^2=(2x-2)^2..

else the values can be checked for the triplets most oftenly used in right angle triangles
3-4-5.. 6-8-10
here we have 6 in choices and fits in perfectly..
A
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Re: In right triangle ABC, x =  [#permalink]

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05 Dec 2015, 11:38
Hi All,

The GMAT is test that is based heavily on patterns. If you know the patterns that frequently occur on the Exam, then you can take advantage of that knowledge to save some time and effort when answering certain questions.

Four types of right triangles are frequently tested on the GMAT: the 30/60/90, 45/45/90, 3/4/5 and 5/12/13. Since this prompt does NOT include angles and the answer choices include MULTIPLES of the 3/4/5, it's HIGHLY LIKELY that this is a 3/4/5 triangle. Using that knowledge, it's not too hard to assign the proper values to the three sides of the triangle and solve for X.

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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** CEO Joined: 12 Sep 2015 Posts: 2713 Location: Canada Re: In right triangle ABC, x = [#permalink] ### Show Tags 05 Dec 2015, 12:34 1 Bunuel wrote: 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 _________________ Brent Hanneson – Founder of gmatprepnow.com Intern Joined: 13 Jun 2011 Posts: 23 Re: In right triangle ABC, x = [#permalink] ### Show Tags 07 Dec 2015, 00:35 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? Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6047 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In right triangle ABC, x = [#permalink] ### Show Tags 07 Dec 2015, 00:48 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: In right triangle ABC, x =  [#permalink]

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07 Dec 2015, 01:02
2
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,
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Re: In right triangle ABC, x =  [#permalink]

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16 Jul 2018, 20:58
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