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# Is x+y<180?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82

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25 May 2016, 18:35
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:19) correct 53% (01:02) wrong based on 76 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.

Attachments

2.png [ 17.47 KiB | Viewed 1009 times ]

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5933 Re: Is x+y<180? [#permalink] ### Show Tags 26 May 2016, 08:57 1 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 Attachments IMG_5632.JPG [ 1.84 MiB | Viewed 944 times ] _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Current Student Status: Persevere Joined: 09 Jan 2016 Posts: 122 Location: Hong Kong GMAT 1: 750 Q50 V41 GPA: 3.52 Is x+y<180? [#permalink] ### Show Tags 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 938 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. Answer - B Edit: Attached the image Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5600 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: Is x+y<180? [#permalink] ### Show Tags 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. _________________ 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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07 Sep 2017, 03:40
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Re: Is x+y<180?   [#permalink] 07 Sep 2017, 03:40
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