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In the figure above, all the marked angles are some multiple of x

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In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post Updated on: 28 Jan 2018, 00:03
2
16
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:59) correct 67% (02:23) wrong based on 320 sessions

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Originally posted by rahul16singh28 on 27 Jan 2018, 21:07.
Last edited by Bunuel on 28 Jan 2018, 00:03, edited 2 times in total.
Renamed the topic and edited the question.
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 27 Jan 2018, 21:48
7
rahul16singh28 wrote:
Please give Kudos, if it helps you in Preparing for GMAT.


An immediate observation...
16x is an angle, so 16x<180.... x<12
Only 8 and 10 are possible..
x=10 can be found from 2nd line and 5th line.
B

Let's check all..
Let number lines 1, 2,3,4,5 from left..
1) let's see 1 PARALLEL to others.
1 ll 2.... x+2x=180...x=60... Not given
1 ll 3.....x=4x....not possible
1 ll 4....x+8x=180...x=20..E
1 ll 5...x=16x...not possible

2) 2
2 ll 3...2x+4x=180...x=30.. not given
2 ll 4 ...2x=8x...not possible
2 ll 5 ...2x+16x=180..x=10..B
3) 3rd
3 ll 4..4x+8x=180....x=15..C
3 ll 5...4x=16x ...not possible
4) 4th
4 ll 5..16x+8x=180... Not possible as X will not be an integer

So possible values of x are 10,15 and 20
But possible is only 10.
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 28 Jan 2018, 10:22
chetan2u wrote:
rahul16singh28 wrote:
Please give Kudos, if it helps you in Preparing for GMAT.


An immediate observation...
16x is an angle, so 16x<180.... x<12
Only 8 and 10 are possible..
x=10 can be found from 2nd line and 5th line.
B

Let's check all..
Let number lines 1, 2,3,4,5 from left..
1) let's see 1 PARALLEL to others.
1 ll 2.... x+2x=180...x=60... Not given
1 ll 3.....x=4x....not possible
1 ll 4....x+8x=180...x=20..E
1 ll 5...x=16x...not possible

2) 2
2 ll 3...2x+4x=180...x=30.. not given
2 ll 4 ...2x=8x...not possible
2 ll 5 ...2x+16x=180..x=10..B
3) 3rd
3 ll 4..4x+8x=180....x=15..C
3 ll 5...4x=16x ...not possible
4) 4th
4 ll 5..16x+8x=180... Not possible as X will not be an integer

So possible values of x are 10,15 and 20
But possible is only 10.



How did you know that 16x is an angle, so 16x<180.... x<12

What is the reasoning behind your solution?

Your help is much appreciated
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 31 Jan 2018, 20:41
1
Quote:
How did you know that 16x is an angle, so 16x<180.... x<12

What is the reasoning behind your solution?

Your help is much appreciated


Hi,
Because the greatest angle is 180 (a line) => 16x is an angel (which is obviously shown in the figure) => 16x must be < 180

Hope it's clear
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 09 Feb 2018, 04:19
Hello, why 15 and 20 are not possible? Thanks
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 20 Feb 2018, 10:07
I am getting confused here. With x=15, the lines with 4x and 8x will also be parallel.

So, why are we bothered about any other line?
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In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 24 Apr 2018, 05:21
I did this,

for lines with angles 4x and 8x to be parallel => 4x + 8x = 12x = 180, x = 15
for lines with angles 2x and 16x to be parallel => 2x + 16x = 18x = 180, x = 10 (minimum so far)
tried with x = 8, found none to be parallel.

So answer (B)
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In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post Updated on: 30 Aug 2018, 18:58
Corrected:

I made table for all values of x and tried searching for equal values in columns A,C and D or in columns B, and E; or Supplementary angles one from either columns A,C, and D; and one from either B, and E.
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Originally posted by Blackishmamba on 23 Aug 2018, 18:23.
Last edited by Blackishmamba on 30 Aug 2018, 18:58, edited 1 time in total.
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 23 Aug 2018, 18:41
hey adkikani Bunuel chetan2u

Can you tell why x = 15, 18 or 20 not possible?

Technically all of them can form an angle with the line (x - axis). Any angle greater than 180 will change the quadrant.

Let me know what is incorrect with my understanding here
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 23 Aug 2018, 22:46
rahul16singh28 wrote:
Image

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The attachment 5033f36b-5ff1-481c-bda2-71f312ce5212.jpg is no longer available


Tricky question and here is why - shown angles are angles between two lines (not line segments). So think about this - how will you show a 320 degrees angle?

Attachment:
angle-320-degrees.png
angle-320-degrees.png [ 3.66 KiB | Viewed 984 times ]

Note that two intersecting lines make 4 angles around the point of intersection such that vertically opposite angles are equal. Can one of the angles be 320 degrees? The other needs to be 320 degrees too. If a is 320, c needs to be 320 too!
Attachment:
images-13.png
images-13.png [ 1.56 KiB | Viewed 984 times ]


Hence, the options (C), (D) and (E) are not possible.

Now it is just about looking for a pair of supplementary angles.
If x = 10, 2x + 16x = 18x = 180
So 2x = 20 degrees and the angle supplementary to 16x would be 20 degrees too making these two lines parallel.

Answer (B)
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Re: In the figure above, all the marked angles are some multiple of x  [#permalink]

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New post 08 Sep 2018, 09:24
IS THIS from gmatprep? pls, shot the screen
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Re: In the figure above, all the marked angles are some multiple of x &nbs [#permalink] 08 Sep 2018, 09:24
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In the figure above, all the marked angles are some multiple of x

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