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# Two person start walking on a road that diverge at angle of 120

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Manager
Joined: 01 Jun 2015
Posts: 230
Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
Two person start walking on a road that diverge at angle of 120  [#permalink]

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12 May 2016, 05:01
3
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:56) correct 27% (02:28) wrong based on 30 sessions

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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

Attachments

GEOMETRY3.jpg [ 8.75 KiB | Viewed 1227 times ]

Manager
Joined: 12 Jun 2015
Posts: 79
Two person start walking on a road that diverge at angle of 120  [#permalink]

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Updated on: 12 May 2016, 06:32
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, 05:52.
Last edited by ronny123 on 12 May 2016, 06:32, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 6548
Two person start walking on a road that diverge at angle of 120  [#permalink]

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12 May 2016, 06:16
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 1196 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

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Joined: 12 Jun 2015
Posts: 79
Re: Two person start walking on a road that diverge at angle of 120  [#permalink]

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12 May 2016, 06:31
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.
Math Expert
Joined: 02 Aug 2009
Posts: 6548
Re: Two person start walking on a road that diverge at angle of 120  [#permalink]

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12 May 2016, 06:37
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

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Joined: 09 Sep 2013
Posts: 7755
Re: Two person start walking on a road that diverge at angle of 120  [#permalink]

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28 Jul 2018, 02:47
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Re: Two person start walking on a road that diverge at angle of 120 &nbs [#permalink] 28 Jul 2018, 02:47
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# Two person start walking on a road that diverge at angle of 120

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