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Math Expert V
Joined: 02 Aug 2009
Posts: 7984
Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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18 00:00

Difficulty:   95% (hard)

Question Stats: 39% (02:21) correct 61% (02:26) wrong based on 181 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

Attachments circular track.png [ 7.9 KiB | Viewed 3827 times ]

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Math Expert V
Joined: 02 Aug 2009
Posts: 7984
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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4
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

D
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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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3
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

Option D
Manager  B
Joined: 07 May 2018
Posts: 61
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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chetan2u wrote:
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

D

Hi,

Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Regards,

Ritvik
Intern  B
Joined: 06 Apr 2018
Posts: 43
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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Hi,
Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Could you please explain how can we know that he travelled 10 miles in the entire track ?

Regards,
Intern  B
Joined: 10 Oct 2017
Posts: 24
GMAT 1: 610 Q41 V35 Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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givinggmat wrote:
Hi,
Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Could you please explain how can we know that he travelled 10 miles in the entire track ?

Regards,

Hi,
I'll try and explain.
since B has travelled only 10 miles while they meet again, means that A is faster than B. We have to find out the ratio of their speeds.
We take an easy assumption as 30 of the length of the track.
So, when A travels 20 B travels 10.
the ratio of their speed is 2:1
so when B travels another 10 miles A would travel 20 in the mean time and they meet gain
CrackVerbal Quant Expert G
Joined: 12 Apr 2019
Posts: 268
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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This is a question based on relative speed concepts which in turn depends on the variation of distance with respect to speed, when time is kept constant.

When the time is constant, distance is directly proportional to speed. In other words, the ratio of distances travelled by two objects will be the same as the ratio of their speeds.

In the question, it’s given that A travelled 20 miles before A and B met each other for the first time. Let us evaluate the statements now.

Using statement I alone, we know the ratio of the speeds. Because both A & B started together and also ended up at the same point (when they met), we can say that they both travelled for the same time.

Because time is constant, the distances travelled by them will be in the same ratio of the speeds. So,

$$D_a$$ : $$D_b$$ = 4:1.

But we know that $$D_a$$ is 20. So, we will be able to find out $$D_b$$. Hence, we will be able to find out one half of the length of the track – this is nothing but the sum of the distances travelled by A and B, right?

Therefore, we will be able to find out the length of the track uniquely (remember that, in DS, you don’t have to go for the exact answer all the time.). So, statement I alone is sufficient. Possible answer options are A or D. Options B, C and E can be eliminated.

Using statement II alone, we know that B has travelled a distance of 10 km by the time they meet for the second time. However, what will remain constant irrespective of the first or the second meeting is the ratio of their speeds.
Let the length of the track be 2πr. Then, distance travelled by A, between the first meeting and the second meeting = 2πr – 10. Now,

$$\frac{(2πr – 10)}{10}$$ = $$\frac{20}{(πr – 20)}$$.

Solving the above equation will definitely help us find a unique value of 2πr. Hence, statement II alone is also sufficient. Option A can be eliminated.

Correct answer option is D.

Although the second statement seems like it is not giving you much information, whatever information it is giving you is enough to solve the question, if you know the ratio concept highlighted throughout the solution.

Hope this helps!
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Intern  B
Joined: 12 Feb 2019
Posts: 1
Re: Two cars A and B start from diametrically opposite points of a circula  [#permalink]

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apurv09 wrote:
givinggmat wrote:
Hi,
Could you please explain the second statement? How did you assume that B travelled 10 miles in this entire track.

Could you please explain how can we know that he travelled 10 miles in the entire track ?

Regards,

Hi,
I'll try and explain.
since B has travelled only 10 miles while they meet again, means that A is faster than B. We have to find out the ratio of their speeds.
We take an easy assumption as 30 of the length of the track.
So, when A travels 20 B travels 10.
the ratio of their speed is 2:1
so when B travels another 10 miles A would travel 20 in the mean time and they meet gain Re: Two cars A and B start from diametrically opposite points of a circula   [#permalink] 10 Jun 2019, 21:23
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