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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 8:18 am

Parallel lines problem:

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Source: Beat The GMAT — Problem Solving | Mon Jan 31, 2011 8:18 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 31, 2011 8:50 am

Refer to the above image.
The red line is parallel to both AB and CD.
Hence,

1. (3x - 20) = y .......... Alternate angles
2. 180 - (5x + 55) = y .......... Alternate angles

Again (y + z) = (3x + 15)

Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 9:26 pm

Does the red line cut that angle in half? ie. Does Y=Z?

[quote="Anurag@Gurome"][url=https://postimage.org/image/2rnxjc3gk/][img]https://s1.postimage.org/2rnxjc3gk/parl.jpg[/img][/url]

Refer to the above image.
The red line is parallel to both AB and CD.
Hence,
[list]1. (3x - 20) = y .......... Alternate angles
2. 180 - (5x + 55) = y .......... Alternate angles[/list]
Again (y + z) = (3x + 15)

Therefore, (3x - 20) + 180 - (5x + 55) = (3x + 15)
=> 5x = 90
=> x = 18[/quote]

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 31, 2011 9:42 pm

yellowho wrote:Does the red line cut that angle in half? ie. Does Y=Z?

Not necessarily.
In fact, if the figure is to scale, then they don't.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jan 31, 2011 9:59 pm

The drawing above shows an alternate approach.

The sum of the angles inside the triangle whose base is on line CD must be 180.

(125-5x) + (165-3x) + (3x-20) = 180
270 - 5x = 180
-5x = -90
x = 18.

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 10:02 pm

Awesome! Love all your alternate approaches to problems Mitch. Can we come up with a new axiom: If Mitch can't come up with an alternate approach thats not math properties heavy, its not a good GMAT problem?

[quote="GMATGuruNY"][url=https://postimage.org/image/2ykbq5ll0/][img]https://s1.postimage.org/2ykbq5ll0/AB_parallel_CD.jpg[/img][/url]

The drawing above shows an alternate approach.

The sum of the angles inside the triangle whose base is on line CD must be 180.

(125-5x) + (165-3x) + (3x-20) = 180
270 - 5x = 180
-5x = -90
x = 18.[/quote]

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