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# What is the value of w in terms of x and y?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
What is the value of w in terms of x and y?  [#permalink]

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19 Mar 2015, 05:07
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3
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:20) correct 34% (02:16) wrong based on 113 sessions

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What is the value of w in terms of x and y? Note: Figure not drawn to scale

A. 2x + 2y - 180
B. 180 - x - y
C. 360 - 2x - 2y
D. 360 - 2x - 3y
E. 180 + x - 2y

Kudos for a correct solution.

Attachment:

originals.jpg [ 19.46 KiB | Viewed 4822 times ]

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Re: What is the value of w in terms of x and y?  [#permalink]

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19 Mar 2015, 05:21
Bunuel wrote:
Attachment:
The attachment originals.jpg is no longer available
What is the value of w in terms of x and y? Note: Figure not drawn to scale

A. 2x + 2y - 180
B. 180 - x - y
C. 360 - 2x - 2y
D. 360 - 2x - 3y
E. 180 + x - 2y

Kudos for a correct solution.

uploaded the image with the solution .
Attachments

gmatclub.jpg [ 43.92 KiB | Viewed 4048 times ]

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Location: United States
Concentration: Strategy, General Management
Re: What is the value of w in terms of x and y?  [#permalink]

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19 Mar 2015, 05:46
The angles of a triangle sums up to 180. A straight line is 180.

the smaller triangle that holds angle w has angles of w, 180-x-y, and 180-x-y.

180 = w + 180-x-y + 180-x-y
w = 2x+2y-180

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Re: What is the value of w in terms of x and y?  [#permalink]

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19 Mar 2015, 19:26
1
Hi All,

For anyone who finds this question 'complex-looking', you can solve it rather easily by TESTing VALUES. There are a few math rules that you have to follow though:

1) The angles in a line sum to 180 degrees
2) The angles in a triangle sum to 180 degrees

Try TESTing a VALUE for X and Y, then fill in all of the various angles in this picture.....You'll end up with a value for W and a way to see if the various answers match.

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Rich
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Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: What is the value of w in terms of x and y?  [#permalink]

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23 Mar 2015, 03:54
Bunuel wrote:

What is the value of w in terms of x and y? Note: Figure not drawn to scale

A. 2x + 2y - 180
B. 180 - x - y
C. 360 - 2x - 2y
D. 360 - 2x - 3y
E. 180 + x - 2y

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

originals (1).jpg [ 20.79 KiB | Viewed 3902 times ]

Here's the same diagram with letters. First of all, look at the big triangle, triangle ACE. We know the three angles in this or any triangle must add up to 180°. Let's say that ∠E = k. Then we know

x + y + k = 180, or k = 180 – x – y

Now, look at the angles around point F. Those three angles form a straight line, that is to say, a 180° angle, so the sum of the three angles there must also be 180°. Since one is x and one is y, the other has to be k --- ∠DFE = k
Attachment:

originals (2).jpg [ 21.54 KiB | Viewed 3899 times ]

Now, look at triangle DEF. The sum of the three angles in this triangle must also be 180°.

w + k + k = 180°

w = 180 – 2k

Now, we have an expression for w in terms of k. To express w in terms of x & y, we need to substitute the expression for k above, k = 180 – x – y

w = 180 – 2(180 – x – y)

w = 180 – 360 + 2x + 2y

w = 2x + 2y – 180

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Re: What is the value of w in terms of x and y?  [#permalink]

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23 Jan 2019, 12:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the value of w in terms of x and y?   [#permalink] 23 Jan 2019, 12:09
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