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# Two persons start walking on a road that diverge at an angle of 120°.

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Manager
Joined: 01 Jun 2015
Posts: 219
Location: India
GMAT 1: 620 Q48 V26
Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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Updated on: 24 Oct 2018, 02:18
7
00:00

Difficulty:

55% (hard)

Question Stats:

68% (03:05) correct 33% (02:13) wrong based on 80 sessions

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Two persons start walking on a road that diverge at an angle of 120°. If they walk at the rate of 3 km/h and 2 km/h respectively. Find the distance between them after 4 hours.

A. 5
B. 4√19
C. 7
D. 8√19
E. √19

Attachment:

2018-10-24_1415.png [ 11.16 KiB | Viewed 388 times ]

Originally posted by techiesam on 12 May 2016, 04:01.
Last edited by Bunuel on 24 Oct 2018, 02:18, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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12 May 2016, 05:37
2
ronny123 wrote:
chetan2u wrote:
techiesam wrote:
Two person start walking on a road that diverge at angle of 120 degree.If they walk at the rate of 2kmph and 3 3kmph relatively, then find the distance between them after 4 hours or find the value of c as given in the image attached below.

A.5
B. 4√19
C.7
D. 8√19
E. √19

hi,

Trignometry is NOT tested in GMAT so there has to be another solution..
SEE att image..
Draw an altitude from A to BC extende at D..
Triangle ACD is a right angle triangle, whose HYP is 2*4..
rest sides are CD-4, opp 30 degree and AD - $$4\sqrt{3}$$, opp 60 degree..

c is hyp..
BD = 3*4 + 4 = 16 and AD = $$4\sqrt{3}$$..
HYp = AC = $$\sqrt{16^2+(4*Sq Root 3})^2$$ = $$\sqrt{304}$$ = $$4\sqrt{19}$$
B

hi,

Don't be offended but isn't the maths inherent to subject correct ?

if you use c^2 = a^2 + b^2 - 2abcos(120)
= a^2 + b^2 - 2ab(-1/2)
= a^2 + b^2 + ab

a = 2 x 4 = 8
b = 3 x 4 = 12
Putting these values,
c^2 = 8^2 + 12^2 + (8)(12)
= 64 +144 + 96
= 304
c = 4√‾19

Saying Trigo isn't tested on the GMAT isn't changing the solution, my friend
Again, no offense meant.

Hi,
It is not meant for you ..
It is for people who are preparing for GMAT so that they do not get into the area where it is NOT required..
You are most welcome to learn anything being tested or not,
BUT people who are interested in just GMAT should not go away with thought that they have to do trignometry to do this Q..

I don't require to take offence or offend you, I am giving the WAY one should think about this solution
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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12 May 2016, 05:16
1
1
techiesam wrote:
Two person start walking on a road that diverge at angle of 120 degree.If they walk at the rate of 2kmph and 3 3kmph relatively, then find the distance between them after 4 hours or find the value of c as given in the image attached below.

A.5
B. 4√19
C.7
D. 8√19
E. √19

hi,

Trignometry is NOT tested in GMAT so there has to be another solution..
SEE att image..
Draw an altitude from A to BC extende at D..
Triangle ACD is a right angle triangle, whose HYP is 2*4..
rest sides are CD-4, opp 30 degree and AD - $$4\sqrt{3}$$, opp 60 degree..

c is hyp..
BD = 3*4 + 4 = 16 and AD = $$4\sqrt{3}$$..
HYp = AC = $$\sqrt{16^2+(4*Sq Root 3})^2$$ = $$\sqrt{304}$$ = $$4\sqrt{19}$$
B
Attachments

IMG_5618.JPG [ 1.75 MiB | Viewed 1902 times ]

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

##### General Discussion
Manager
Joined: 12 Jun 2015
Posts: 79
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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Updated on: 12 May 2016, 05:32
hi techiesam,

can you please check if the question is correct, specifically whether one of the speeds is 3 kmph or 33 kmph
Also,
you can simply use the following formula for cos x to get your answer :

c^2 = a^2 + b^2 - 2abcos(120)
= a^2 + b^2 - 2ab(-1/2)
= a^2 + b^2 + ab

Originally posted by ronny123 on 12 May 2016, 04:52.
Last edited by ronny123 on 12 May 2016, 05:32, edited 1 time in total.
Manager
Joined: 12 Jun 2015
Posts: 79
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

### Show Tags

12 May 2016, 05:31
chetan2u wrote:
techiesam wrote:
Two person start walking on a road that diverge at angle of 120 degree.If they walk at the rate of 2kmph and 3 3kmph relatively, then find the distance between them after 4 hours or find the value of c as given in the image attached below.

A.5
B. 4√19
C.7
D. 8√19
E. √19

hi,

Trignometry is NOT tested in GMAT so there has to be another solution..
SEE att image..
Draw an altitude from A to BC extende at D..
Triangle ACD is a right angle triangle, whose HYP is 2*4..
rest sides are CD-4, opp 30 degree and AD - $$4\sqrt{3}$$, opp 60 degree..

c is hyp..
BD = 3*4 + 4 = 16 and AD = $$4\sqrt{3}$$..
HYp = AC = $$\sqrt{16^2+(4*Sq Root 3})^2$$ = $$\sqrt{304}$$ = $$4\sqrt{19}$$
B

hi,

Don't be offended but isn't the maths inherent to subject correct ?

if you use c^2 = a^2 + b^2 - 2abcos(120)
= a^2 + b^2 - 2ab(-1/2)
= a^2 + b^2 + ab

a = 2 x 4 = 8
b = 3 x 4 = 12
Putting these values,
c^2 = 8^2 + 12^2 + (8)(12)
= 64 +144 + 96
= 304
c = 4√‾19

Saying Trigo isn't tested on the GMAT isn't changing the solution, my friend
Again, no offense meant.
Director
Joined: 27 May 2012
Posts: 606
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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19 Oct 2018, 05:31
1
techiesam wrote:
Two person start walking on a road that diverge at angle of 120 degree.If they walk at the rate of 2kmph and 3 3kmph relatively, then find the distance between them after 4 hours or find the value of c as given in the image attached below.

A.5
B. 4√19
C.7
D. 8√19
E. √19

Dear Moderator,
There is a typo in this question, the latter speed seems to be 3 kmph rather than 33 kmph, hope you will do the needful. Thank you.
_________________

- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 50615
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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24 Oct 2018, 02:19
stne wrote:
techiesam wrote:
Two person start walking on a road that diverge at angle of 120 degree.If they walk at the rate of 2kmph and 3 3kmph relatively, then find the distance between them after 4 hours or find the value of c as given in the image attached below.

A.5
B. 4√19
C.7
D. 8√19
E. √19

Dear Moderator,
There is a typo in this question, the latter speed seems to be 3 kmph rather than 33 kmph, hope you will do the needful. Thank you.

________________
Edited. Thank you.
_________________
Manager
Joined: 21 Jun 2017
Posts: 135
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: Two persons start walking on a road that diverge at an angle of 120°.  [#permalink]

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24 Oct 2018, 05:07
Longest side will be opposite to angle C. This means c should be more than 12.
Also by triangle property
4<c<20
Combining,
12<c<20.
PS: sqrt 19 is almost 4.5

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_________________

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Re: Two persons start walking on a road that diverge at an angle of 120°. &nbs [#permalink] 24 Oct 2018, 05:07
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