It is currently 23 Feb 2018, 16:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 5660
Two cars A and B start from diametrically opposite points of a circula [#permalink]

### Show Tags

13 Jan 2018, 04:28
00:00

Difficulty:

85% (hard)

Question Stats:

39% (01:24) correct 61% (02:14) wrong based on 48 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Attachments

circular track.png [ 7.9 KiB | Viewed 422 times ]

_________________

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

BANGALORE/-

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 939
Location: India
GPA: 3.82
Re: Two cars A and B start from diametrically opposite points of a circula [#permalink]

### Show Tags

13 Jan 2018, 10:44
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
Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: Two cars A and B start from diametrically opposite points of a circula [#permalink]

### Show Tags

13 Jan 2018, 21:52
Expert's post
2
This post was
BOOKMARKED
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
_________________

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

BANGALORE/-

Re: Two cars A and B start from diametrically opposite points of a circula   [#permalink] 13 Jan 2018, 21:52
Display posts from previous: Sort by