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

Question

https://gmatclub.com/forum/download/file.php?id=39739 5033f36b-5ff1-481c-bda2-71f312ce5212.jpg

chetan2u · Accepted Answer

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.

Blackishmamba · Answer

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.

mekoner · Answer

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

lichting · Answer

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

krikre · Answer

Hello, why 15 and 20 are not possible? Thanks

Nived · Answer

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?

hellosanthosh2k2 · Answer

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)

pikolo2510 · Answer

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

KarishmaB · Answer

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? angle-320-degrees.png 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! images-13.png 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)

tinytiger · Answer

Hmmn my approach was to not be distracted by the picture and was similar to what was discussed above.

1) Look at the properties of parallel lines - for 2 lines to be parallel, there must be a perpendicular line joining these two lines (whether it's |--| or crossing both lines i.e. --|--|--).

2) Any angle subtended by the perpendicular line, would have be 90 degrees.

3) With this, I tried adding the different x's together with the following:
a) x + 2x = 180, x = 60 (not in answer choice, immediately calibrate approach by trying combination of x's that can give me 180 degrees)
b) 2x + 16x = 180 --> x = 10

Answer: B.

rnn · Answer

16x is an angle, so 16x<180.... x<12

I do not understand this statement. my assumption would have been that 16x<=90 not 180

tinytiger · Answer

Hi  nausherwan , I think the key is not to be distracted by how the initial diagram is being drawn (definitely not to scale). The key principle to follow here is that opposite complementary angles split by a straight line (or lines) should add up to be 180 degrees. There are different combinations that can be explored in the diagram above, so it's about finding one that works AND that is stated in the answer choice.

Hope this clarifies.

-tinytiger

Aabhash777 · Answer

DO these questions still appear in Focus GMAT?  KarishmaB   Bunuel

Bunuel · Answer

I'd say it's unlikely because of the geometry content.

bumpbot · Answer

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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

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