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Two cars A and B start from diametrically opposite points of a circula

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Two cars A and B start from diametrically opposite points of a circula [#permalink]

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New post 13 Jan 2018, 05:28
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  95% (hard)

Question Stats:

40% (01:40) correct 60% (02:06) wrong based on 71 sessions

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Two cars A and B start at same time from diametrically opposite points of a circular track in opposite direction, with A moving clockwise and B moving anti-clockwise. If they meet each other for first time after A has traveled 20 miles, what is the length of circular track?

(1) The ratio of speed of A to B is 4:1.
(2) they meet again after B has traveled 10 miles.


New tricky question

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Re: Two cars A and B start from diametrically opposite points of a circula [#permalink]

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New post 13 Jan 2018, 11:44
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chetan2u wrote:
Two cars A and B start from diametrically opposite points of a circular track in opposite direction, with A moving clockwise and B moving anti-clockwise. If they meet each other for first time after A has traveled 20 miles, what is the length of circular track?

(1) The ratio of speed of A to B is 4:1.
(2) they meet again after B has traveled 10 miles.


New tricky question


Let the speed of A & B be \(u\) & \(v\) respectively. To start with as they are moving towards each other from diametrically opposite points, hence when they will meet they would have covered half of the circumference.

\(=>πr=(u+v)*t\), where \(t\) is the time take to meet

given \(t=\frac{20}{u}\)

so \(πr=(u+v)*\frac{20}{u}\)-------------------(1)

Hence length of circular track i.e. the circumference, \(2πr=40+40\frac{v}{u}\)

Therefore we need the ratio of speeds of A & B to know the length

Statement 1: directly provides the ratio. Sufficient

Statement 2: When they meet the second time, they would have traveled the complete circular path and time take is \(\frac{10}{v}\)

so \(2πr=(u+v)*\frac{10}{v}\), divide this by equation (1) to get

\(2=\frac{10u}{20v}=>\frac{v}{u}=\frac{1}{4}\). Hence we have the ratio of speeds. Sufficient

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Re: Two cars A and B start from diametrically opposite points of a circula [#permalink]

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New post 13 Jan 2018, 22:52
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1
chetan2u wrote:
Two cars A and B start at the same time from diametrically opposite points of a circular track in opposite direction, with A moving clockwise and B moving anti-clockwise. If they meet each other for first time after A has traveled 20 miles, what is the length of circular track?

(1) The ratio of speed of A to B is 4:1.
(2) they meet again after B has traveled 10 miles.


New tricky question



Apart from the above method , a very logical and easy method would be " To work for the distance traveled as a part of total when they meet."

FIRST meeting -
when they both meet first, both have traveled HALF the length of track.
Let B travel x, and A travels 20, so half track = x+20
and total = 2(x+20)

lets see the statements-

(1) The ratio of speed of A to B is 4:1.
When they meet for the first time, both have traveled for SAME time.
so if A travels 20 miles and the A:B speed ratio is 4:1, B will travel \(\frac{20}{4}=5\) miles.
so HALF track = \(20+x=20+5=25\)
full track = \(2*25=50..\)
sufficient

(2) they meet again after B has traveled 10 miles.
This is TRICKY part
How much have they traveled when they meet for second time? - They travel a full track after the first meeting..
In this entire track, B travels 10 miles, so in half track he would cover \(\frac{10}{2} = 5\) miles..
so combined half track = \(20+5=25..\)
full track = \(2*25=50\) miles
sufficient

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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: Two cars A and B start from diametrically opposite points of a circula   [#permalink] 13 Jan 2018, 22:52
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