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655-705 Level|   Geometry|      
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systemm6665
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In the figure above, does a = b? Updated on: 28 Apr 2014, 02:45
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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C
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55% (hard)

Question Stats:

49% (01:21) correct 51% (01:12) wrong based on 297 sessions

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In the figure above, does a = b?

(1) x = y

(2) c = x
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C
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Bunuel
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In the figure above, does a = b? 28 Apr 2014, 02:54
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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: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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In the figure above, does a = b? 28 Apr 2014, 06:56
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Thank you Bunuel. I will keep the topic name in mind for the next post. :)
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In the figure above, does a = b? 29 Apr 2014, 04:55
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Bunuel

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: rules-for-posting-please-read-this-before-posting-133935.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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In the figure above, does a = b? 29 Apr 2014, 07:13
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maaadhu
Bunuel

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: rules-for-posting-please-read-this-before-posting-133935.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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In the figure above, does a = b? 07 Oct 2014, 05:15
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Doesn't B imply that the two horizontal lines are parallel?
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In the figure above, does a = b? 07 Oct 2014, 07:31
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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:
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In the figure above, does a = b? 07 Oct 2014, 11:04
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kamranjkhan

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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In the figure above, does a = b? 30 Jul 2015, 08:04
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Bunuel

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: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi Bunuel,

One Q. If we consider only second statement i.e. c=x

This means, b= 180-x (straight lines, b+c=180)

Also, y= 180-x, 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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In the figure above, does a = b? 30 Jul 2015, 08:13
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Bunuel

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: rules-for-posting-please-read-this-before-posting-133935.html Thank you.



Hi Bunuel,

One Q. If we consider only second statement i.e. c=x

This means, b= 180-x (straight lines, b+c=180)

Also, y= 180-x, 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

Non-adjacent 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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In the figure above, does a = b? 30 Jul 2015, 10:42
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Attachment:
gmat.jpg
In the figure above, does a = b?

(1) x = y

(2) c = x

Statement 1: x = y
To 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 SUFFICIENT

Statement 2: c = x
Since, 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 SUFFICIENT

Combining the two statements
x = y = c = a = 90 degrees [because x+y = 180]
and a + b = 180
i.e. b = 90 = a
SUFFICIENT

Answer: option C
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In the figure above, does a = b? 07 Aug 2016, 12:35
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systemm6665
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? 07 Aug 2016, 14:05
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systemm6665
Show SpoilerImage
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

Show Spoiler
(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
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In the figure above, does a = b? 23 Apr 2023, 21:15
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GMATNinja it seems like sometimes we can assume that we can trust the way the image is drawn and sometimes we cannot, such as with this question (i cant find an example of the former case, but I've seen it exist). Is there a way to tell whether we should trust or not trust the picture?
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In the figure above, does a = b? 23 Apr 2023, 23:47
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gmattyfatty
GMATNinja it seems like sometimes we can assume that we can trust the way the image is drawn and sometimes we cannot, such as with this question (i cant find an example of the former case, but I've seen it exist). Is there a way to tell whether we should trust or not trust the picture?

Check the instructions you get before the exam:







I'd advice to familiarize yourselves with the above, especially pay attention to the parts in red boxes.

Here is a part you are interested in:

    For all questions in the Quantitative section you may assume the following:
      Numbers:
    • All numbers used are real numbers.

      Figures:
    • For Problem Solving questions, figures are drawn as accurately as possible. Exceptions will be clearly noted.
    • For Data Sufficiency questions, figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
    • Lines shown as straight are straight, and lines that appear jagged are also straight.
    • The positions of points, angles, regions, etc. exist in the positing shown, and angle measures are greater than zero.
    • All figures lie in a plane unless otherwise indicated.


Hope it helps.
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