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# In the figure above, does a = b?

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In the figure above, does a = b?  [#permalink]

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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

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?  [#permalink]

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28 Apr 2014, 02:54
2

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.

Hope it's clear.

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Re: In the figure above, does a = b?  [#permalink]

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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?  [#permalink]

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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.

Hope it's clear.

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?  [#permalink]

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29 Apr 2014, 07:13
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.

Hope it's clear.

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?  [#permalink]

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07 Oct 2014, 05:15
1
Doesn't B imply that the two horizontal lines are parallel?
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Re: In the figure above, does a = b?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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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.

Hope it's clear.

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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Re: In the figure above, does a = b?  [#permalink]

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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.

Hope it's clear.

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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Re: In the figure above, does a = b?  [#permalink]

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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 = 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

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Re: In the figure above, does a = b?  [#permalink]

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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?  [#permalink]

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07 Aug 2016, 14:05
systemm6665 wrote:
Spoiler: :: Image

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?  [#permalink]

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01 Feb 2019, 10:06
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Re: In the figure above, does a = b?   [#permalink] 01 Feb 2019, 10:06
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