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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 27 Jan 2018, 20:07
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Last edited by Bunuel on 27 Jan 2018, 23:03, edited 2 times 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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rahul16singh28 wrote:
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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, 09:22
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, 19:41
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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, 03:19
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, 09:07
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?
Re: In the figure above, all the marked angles are some multiple of x   [#permalink] 20 Feb 2018, 09:07
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In the figure above, all the marked angles are some multiple of x

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