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25 May 2016, 18:35
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
51% (01:55) correct
49%
(01:27)
wrong
based on 106
sessions
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Not Attempted Yet
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.
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 3100 times ]
26 May 2016, 08:57
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MathRevolution
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 2967 times ]
26 May 2016, 09:52
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MathRevolution
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 2984 times ]
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
Moderator Note: Attached the image
