Last visit was: 19 Nov 2025, 12:16 It is currently 19 Nov 2025, 12:16
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,337
 [4]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,337
 [4]
Points A, P, Q and B lie on the same line such that P, Q and B are, re 03 Apr 2020, 08:55
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

80% (02:41) correct 20% (02:33) wrong based on 60 sessions

History

Date
Time
Result
Not Attempted Yet
Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 17 Jul 2025
Posts: 3,086
Own Kudos:
3,103
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,086
Kudos: 3,103
Points A, P, Q and B lie on the same line such that P, Q and B are, re 03 Apr 2020, 09:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Speed is direct proportional to distance.
Car 3 cover 100m when Car 1 covered 200.-----(1)
Also, Car 3 covered 200m when Car 2 does 100m. ------(2)
So, the ratio will be Car1:Car2:Car3
400:100:200 (equating statements)
So the ratio of speed of Car 2 : Car 1 is 1:4
So OA is A

Posted from my mobile device
User avatar
preetamsaha
User avatar
Joined: 14 Oct 2019
Last visit: 18 Jan 2025
Posts: 337
Own Kudos:
541
Given Kudos: 127
Status:Today a Reader; Tomorrow a Leader.
Location: India
GPA: 4
WE:Engineering (Energy)
Posts: 337
Kudos: 541
Points A, P, Q and B lie on the same line such that P, Q and B are, re 03 Apr 2020, 14:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Car 3 meets car 1 at Q, which is 200 km from A.

Therefore, at the time of their meeting car 1 must have travelled 200 km and car 3 must have travelled 100 km.

As the time is same, ratio of speed of car 1 to speed of car 3 = 2 : 1.

Car 3 meets car 2 at P, which is 100 km from A.

Therefore, at the time of their meeting car 2 must have travelled 100 km and car 3 must have travelled 200 km.

As the time is same, ratio of speed of car 2 to speed of car 3 = 1 : 2.

Speed of car 1 : speed of car 3 = 2 : 1

And speed of car 2 : speed of car 3 = 1 : 2

So, speed of car 1 : speed of car 2 : speed of car 3 = 4 : 1 : 2

speed of car 2 : speed of car 1 = 1 : 4

correct answer is A
User avatar
preetamsaha
User avatar
Joined: 14 Oct 2019
Last visit: 18 Jan 2025
Posts: 337
Own Kudos:
541
Given Kudos: 127
Status:Today a Reader; Tomorrow a Leader.
Location: India
GPA: 4
WE:Engineering (Energy)
Posts: 337
Kudos: 541
Points A, P, Q and B lie on the same line such that P, Q and B are, re 03 Apr 2020, 15:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
method II : let , speed of car 1,2,3 be v1,v2,v3 respectively.
from s=vt formula,
200/v1 = 100/v3 ___________ (1)
100/v2 = 200/v3 ___________(2)
from (1) and (2)
v2/v1 = 1: 4 [ANSWER A ]
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
Points A, P, Q and B lie on the same line such that P, Q and B are, re 04 Apr 2020, 01:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9


Are You Up For the Challenge: 700 Level Questions
Show more

Solution



    • Let the speed of car 1, car 2 and car 3 be \(s_1, s_2\) and \(s_3 \)respectively.
    • We know that \(distance = speed * time\),
      o And if time is constant, speed is directly proportional to distance.
    • Now, Car 1 and Car 3 meets at Q.
      o Since, both started simultaneously, time is constant.
      o Thus, Ratio of speed of car 1 and car 2 = Ratio of distance travelled by car 1 and car 2,
         \(s_1 : s_3 = 200:100 = 2:1 …………Eq.(i)\)
    • Also, Car 2 and Car 3 meets at P,
      o Again, both started at same time, so time is constant.
      o Thus, Ratio of speed of car 3 and car 2 = Ratio of distance travelled by car 3 and car 2,
         \(s_3 : s_2 = 200:100 = 2:1 …………Eq.(ii)\)
    • Now, to equate the ratios, we can rewrite Eq.(i) as
      o \(s_1 : s_3 = 2:1 = 4:2\)
    • Now, from the above equation and eq.(ii), we get,
      o \(s_1 : s_3: s_2 = 4 : 2 :1\)
         \(s_2 : s_1 = 1:4\)
Thus, the correct answer is Option A.
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 19 Nov 2025
Posts: 5,794
Own Kudos:
5,510
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,794
Kudos: 5,510
Points A, P, Q and B lie on the same line such that P, Q and B are, re 04 Apr 2020, 09:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

A. 1 : 4
B. 2 : 9
C. 1 : 2
D. 2 : 7
E. 2 : 9


Are You Up For the Challenge: 700 Level Questions
Show more


Given: Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P.

Asked: If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is


A------100 km----------P---------100 km--------Q----------100 km----------B
Car1->----------------------------------------Car1+3
Car2->----------------Car2+3
-----------------------------------------------------------------------------<-Car 3

Since all cars start at the same time, once they meet their speeds are directly proportional to the distance covered.

Let the speed of car1 , car2 & car3 be v1, v2 & v3 respectively

v1/v3 = 200/100 = 2/1 = 2
v2/v3 = 100/200 = 1/2

v2/v1 = (v2/v3)/(v1/v3) = (1/2)/2 = 1/4

IMO A
avatar
fireagablast
avatar
Joined: 30 Jun 2019
Last visit: 17 Aug 2021
Posts: 263
Own Kudos:
123
Given Kudos: 8
Posts: 263
Kudos: 123
Points A, P, Q and B lie on the same line such that P, Q and B are, re 04 Apr 2020, 13:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Car1 goes 200, Car 3 goes 100
Car 3 goes 200, Car 2 goes 100

C1:C3 = 2:1
C3:C2 = 2:1

C1:C3:C2 = 2:1 2:1 = 4:2 2:1 = 4:2:1
C1:C2 = 4:1
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
Points A, P, Q and B lie on the same line such that P, Q and B are, re 19 Feb 2024, 03:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts