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# In the diagram above, BC is parallel to DE

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Magoosh GMAT Instructor
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In the diagram above, BC is parallel to DE [#permalink]

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05 Mar 2013, 15:40
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right triangle with parallel segment.JPG [ 16.91 KiB | Viewed 3674 times ]

In the diagram above, BC is parallel to DE, DE = 20, and AC = CE = 6. What is the length of AB?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

For a full explanation, and thoughts about similar triangles, see the following post:
http://magoosh.com/gmat/2013/gmat-math-similar-shapes/

Mike
[Reveal] Spoiler: OA

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Mike McGarry
Magoosh Test Prep

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Re: In the diagram above, BC is parallel to DE [#permalink]

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07 Mar 2013, 00:37
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Ans = 8 (B)

20 ^ 2 = 12 ^ 2 + x ^ 2

x ^ 2 = 256; x = 16

16/2 (as it bisected) = 8
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Re: In the diagram above, BC is parallel to DE [#permalink]

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08 Mar 2013, 13:37
somalwar wrote:
Ans = 8 (B)

20 ^ 2 = 12 ^ 2 + x ^ 2

x ^ 2 = 256; x = 16

16/2 (as it bisected) = 8

I took too much time. Can someone please show me some short cuts to breaking this down to 16 quicker?

20 ^ 2 = 12 ^ 2 + x ^ 2

I did:
400=144-x^2
256=x^2

Getting the square root of 256 took me a while. These are the little calculations that are making me trip up and take so much time even on the easier questions.
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If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

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Re: In the diagram above, BC is parallel to DE [#permalink]

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08 Mar 2013, 13:54
DelSingh wrote:
somalwar wrote:
Ans = 8 (B)

20 ^ 2 = 12 ^ 2 + x ^ 2

x ^ 2 = 256; x = 16

16/2 (as it bisected) = 8

I took too much time. Can someone please show me some short cuts to breaking this down to 16 quicker?

20 ^ 2 = 12 ^ 2 + x ^ 2

I did:
400=144-x^2
256=x^2

Getting the square root of 256 took me a while. These are the little calculations that are making me trip up and take so much time even on the easier questions.

Since ADE and ABC are similar triangles(AC=CE and angles are equal),BC will be half of DE i.e BC = 10.

Using pythagorean theorem, solve for AB -

10^2 = 6^2+ AB ^2 which gives AB = 8.

Its useful to learn the pythogorean numbers to improve your speed -

3,4,5
6,8,10
5,12,13
8,15,17

and their respective multiples.

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4426

Kudos [?]: 8453 [1], given: 102

Re: In the diagram above, BC is parallel to DE [#permalink]

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14 Mar 2013, 12:08
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gmatgooner wrote:
DelSingh wrote:
I took too much time. Can someone please show me some short cuts to breaking this down to 16 quicker? Getting the square root of 256 took me a while. These are the little calculations that are making me trip up and take so much time even on the easier questions.

Its useful to learn the pythagorean numbers to improve your speed - and their respective multiples.

I agree with gmatgooner's good advice to DelSingh.

First of all, here's a blog that discusses the Pythagorean triplets:
http://magoosh.com/gmat/2012/pythagorea ... -the-gmat/

DelSingh, I would say --- proportional reasoning is one of the BIGGEST shortcuts on the entire math section. Always be on the lookout for time-saving proportion tricks.

You were looking at a right triangle with sides 12 - x - 20, and you needed to use the Pythagorean Theorem to find the x. It's pure insanity to plug those numbers in as is and do the calculation without a calculator! Even if there's no smaller triangle in the diagram, use proportions. The GCF of 12 & 20 is 4, so imagine scaling down the triangle by this GCF --- the new imaginary triangle is 3 - y - 5. Now, even if you don't know your Pyth. Triplets, it's ridiculously easy to do the math to figure out that y = 4. Once you have that, simply scale back up by multiplying by 4, the number by which we divided --- 4*4 = 16 ---- that's a route to get to 16 that doesn't involve much beyond single digit multiplication.

As a general rule, if you are doing any math calculations for GMAT problems that gets you into three-digit numbers, you almost definitely are doing too much work, and there's some enormously important simplification move that you are overlooking. If you have other problems on which you don't see how to avoid three-digit calculations, those would be excellent questions in this forum --- how to do the problem with less complicated arithmetic?

Does that make sense?

Mike
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Mike McGarry
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Re: In the diagram above, BC is parallel to DE [#permalink]

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05 Sep 2014, 22:23
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Re: In the diagram above, BC is parallel to DE   [#permalink] 05 Sep 2014, 22:23
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