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# Is x+y<180?

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Math Revolution GMAT Instructor
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25 May 2016, 18:35
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46% (01:16) correct 54% (01:04) wrong based on 67 sessions

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Is x+y<180?
1) Line a and line b are NOT parallel
2) r+q>180

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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26 May 2016, 08:57
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MathRevolution wrote:
Is x+y<180?
1) Line a and line b are NOT parallel
2) r+q>180

*An answer will be posted in 2 days.

Pl see the attached image...
and mark s and t as shown...

1) Line a and line b are NOT parallel
We can ONLY say $$x+y\neq{180}$$..
Insuff

2) $$r+q>180$$
q is an interior angle and would be equal to s+t....
$$r+q = r+s+t...... r+s =180-x$$and $$t = 180-y$$...
so $$r+s+t = 180-x+180-y$$.....
$$r+q>180.....................360-(x+y) > 180.......x+y<360-180......................x+y<180$$
Suff

B
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26 May 2016, 09:52
MathRevolution wrote:
Is x+y<180?
1) Line a and line b are NOT parallel
2) r+q>180

*An answer will be posted in 2 days.

Statement 1
Line a and line b are NOT parallel
If line a and b had been parallel then x + y would have been 180
Since it is given that a and b are not parallel, there are two possible situations as seen in the attached image.
Attachment:

Solution.png [ 10.94 KiB | Viewed 765 times ]

Situation 1: lines a and b are converging towards each other as we move from left to right
In this situation x + y will always be less than 180. (Note: r + q > 180)
Situation 2: lines a and b are moving away from each other as we move from left to right
In this situation x + y will always be greater than 180. (Note: r + q < 180)
So, statement 1 is insufficient

Statement 2
r+q>180
If r + q had been equal to 180, then a and b would have been parallel.
As r+q>180, a and b are not parallel.
So we could have had the same 2 situations as in statement 1 above.
But we know that r+q>180 and this is only possible in situation 1 , i.e.lines a and b converge towards each other as we move from left to right.
In this situation, x + y will always be less than 180
Hence, this statement is sufficient.

Edit: Attached the image

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28 May 2016, 19:45
If we modify the original condition and the question, if line a and b are parallel, x+y=180. x+y<180? Is asking if line a and line b meets. This means r+q>180. Hence, the correct answer is B.
- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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07 Sep 2017, 03:40
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Re: Is x+y<180?   [#permalink] 07 Sep 2017, 03:40
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# Is x+y<180?

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