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In the figure above, does a = b?
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Updated on: 28 Apr 2014, 02:45
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In the figure above, does a = b? (1) x = y (2) c = x
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Originally posted by systemm6665 on 27 Apr 2014, 07:52.
Last edited by Bunuel on 28 Apr 2014, 02:45, edited 1 time in total.
Renamed the topic and edited the question.



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Re: In the figure above, does a = b?
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28 Apr 2014, 02:54
In the figure above, does a = b?(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) > y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient. (2) c = x. Clearly insufficient. (1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient. Answer: C. Hope it's clear. P.S. Please name the topics properly. Rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you.
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Re: In the figure above, does a = b?
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28 Apr 2014, 06:56
Thank you Bunuel. I will keep the topic name in mind for the next post.



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Re: In the figure above, does a = b?
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29 Apr 2014, 04:55
Bunuel wrote: In the figure above, does a = b?(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) > y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient. (2) c = x. Clearly insufficient. (1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient. Answer: C. Hope it's clear. P.S. Please name the topics properly. Rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you. Bunuel, Isnt B sufficient? If C = x, then it will be the case where parallel lines bisected by the middle line. if parallel lines are bisected, isnt a= b? Please let me know why I am wrong?
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Re: In the figure above, does a = b?
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29 Apr 2014, 07:13
maaadhu wrote: Bunuel wrote: In the figure above, does a = b?(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) > y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient. (2) c = x. Clearly insufficient. (1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient. Answer: C. Hope it's clear. P.S. Please name the topics properly. Rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you. Bunuel, Isnt B sufficient? If C = x, then it will be the case where parallel lines bisected by the middle line. if parallel lines are bisected, isnt a= b? Please let me know why I am wrong? We don't know whether the lines are parallel. What do you mean by "bisected"?
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Re: In the figure above, does a = b?
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07 Oct 2014, 05:15
Doesn't B imply that the two horizontal lines are parallel?



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Re: In the figure above, does a = b?
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07 Oct 2014, 07:31
kamranjkhan wrote: Doesn't B imply that the two horizontal lines are parallel? No. It implies that they are at the same angle to "vertical" line: since x = a and c = x, then c = a. Check an example below: Attachment:
Untitled.png [ 1.76 KiB  Viewed 3538 times ]
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Re: In the figure above, does a = b?
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07 Oct 2014, 11:04
Bunuel wrote: kamranjkhan wrote: Doesn't B imply that the two horizontal lines are parallel? No. It implies that they are at the same angle to "vertical" line: since x = a and c = x, then c = a. Check an example below: Attachment: Untitled.png Thanks! I got it horribly wrong.



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Re: In the figure above, does a = b?
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30 Jul 2015, 08:04
Bunuel wrote: In the figure above, does a = b?(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) > y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient. (2) c = x. Clearly insufficient. (1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient. Answer: C. Hope it's clear. P.S. Please name the topics properly. Rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you. Hi Bunuel, One Q. If we consider only second statement i.e. c=x This means, b= 180x (straight lines, b+c=180) Also, y= 180x, this implies that a=x. From here we can easily deduce that a and b are not equal. Can you please tell me where exactly I have gone wrong ? Thanks, Gaurav



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Re: In the figure above, does a = b?
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30 Jul 2015, 08:13
GauravSolanky wrote: Bunuel wrote: In the figure above, does a = b?(1) x = y. This implies that x = y = 90° (straight line is 180°, hence each must be 90°) > y = a = 90° (straight line is 180°, hence each must be 90°). So, the question asks whether a = b = 90°. Rotation of the lower line changes the measure of angle b, so there is no way to determine whether it's 90°. Not sufficient. (2) c = x. Clearly insufficient. (1)+(2) Since from (2) c = x, then from (1) c = x = y = 90°. Now, if c = 90°, then b = 90° too. Therefore a = b = 90°. Sufficient. Answer: C. Hope it's clear. P.S. Please name the topics properly. Rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you. Hi Bunuel, One Q. If we consider only second statement i.e. c=x This means, b= 180x (straight lines, b+c=180) Also, y= 180x, this implies that a=x. From here we can easily deduce that a and b are not equal. Can you please tell me where exactly I have gone wrong ? Thanks, Gaurav Nonadjacent angles formed by the intersection of two straight lines are always equal, so a = x regardless whether c = x. Also, I don't understand how you got that " we can easily deduce that a and b are not equal". Consider the simplest example to prove that a can be equal to b: a = b = c = x = y = 90 degrees.
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Re: In the figure above, does a = b?
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30 Jul 2015, 10:42
systemm6665 wrote: Attachment: gmat.jpg In the figure above, does a = b? (1) x = y (2) c = x Statement 1: x = yTo establish the comparison between angles a and b we need to establish the relation between one of the angles {x, y, a} and {b, c} First statement doesn't establish relationship between the two sets of angles. Hence, NOT SUFFICIENTStatement 2: c = xSince, Angle x = Angle a [Vertically Opposite angles] and c = x therefore c = x = a but, c+b = 180 i.e. a + b = 180 but a and b may or may NOT be equal.Hence, NOT SUFFICIENTCombining the two statements x = y = c = a = 90 degrees [because x+y = 180] and a + b = 180 i.e. b = 90 = a SUFFICIENTAnswer: option C
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Re: In the figure above, does a = b?
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07 Aug 2016, 12:35
systemm6665 wrote: Attachment: gmat.jpg In the figure above, does a = b? (1) x = y (2) c = x we can write x+y=180 y+a=180 x+y=y+a x=a..... Also as C+B=180 and Y+A=180 means C+B=Y+A(a) using both statements we can write Y=X=C substituting in (a) we get A=B suff.. Ans C



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In the figure above, does a = b?
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07 Aug 2016, 14:05
systemm6665 wrote: In the figure above, does a = b? \(a = x\) \(y = 180  x\) \(b = 180  c\) \(\textbf{(1) } x = y\) \(a = x = y = 90\) We know nothing of the angle between \(b\) and \(c\) (the lines do not need to be parallel) Insufficient\(\textbf{(2) } c = x\) \(b = 180  c \implies b = 180  a\) \(a = 90 \implies b = a\\ a \neq 90 \implies b \neq a\) Insufficient\(b = 180  a\\ a = 90\\ \therefore b = a\) Sufficient(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
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Re: In the figure above, does a = b?
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01 Feb 2019, 10:06
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Re: In the figure above, does a = b?
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