Instead of calculating the ratio through algebra, this approach felt faster to me -
Observation 1 - Since A has to land back into it's starting position after 3 laps, the speed of A is a number divisible by 3. You can add all ratios given in each option and check the sum of the three ratios given (ratio1:ratio2:ratio3) should be divisible by 3, that narrows down our possible answer choices to C,D and E.
Now you can pick each Ratio and apply both scenarios and see what are the relative positions coming for A, B, C in each scenario. For instance -
Picking C (4:3:2) -
We know A will always come back to it's starting position so it's easier to comprehend the relative position w.r.t A, therefore we can write the ratio as 1:3/4:2/4. Notice that this is exactly satisfies scenario 1 - "They start at the same time, from the same point and run in the same direction. A is the quickest and when A finishes the first lap lap, C is as much behind B as B is behind A."
If we multiply this ratio by 3 = 3: 9/4 : 3/2, B should have been at A's starting position (should be a whole number)
Therefore we can eliminate C.
Picking E (3:2:1) -
E = 1 : 2/3 : 1/3 (this also perfectly satisfies scenario 1)
Let's multiply the ratio by 3 and see what are the relative positions of A, B and C -
E' = 3 : 2 : 1 (B comes to A starting position, however C also comes at the came exact position since it's a whole number. But Scenario to explains that C should have been on B's place aka 2/3rd mark of the circle)
Therefore we can eliminate E.
We are left with D, which is our answer.
GMATinsight
Bunuel
Three friends A, B and C decide to run around a circular track. They start at the same time, from the same point and run in the same direction. A is the quickest and when A finishes the first lap lap, C is as much behind B as B is behind A. When A completes 3 laps, C is at the exact same point on the circular track as B was when A finished the first lap. What is the ratio of the speeds of A, B and C?
A. 6 : 5 : 3
B. 5 : 4 : 2
C. 4 : 3 : 2
D. 5 : 4 : 3
E. 3 : 2 : 1
Are You Up For the Challenge: 700 Level QuestionsHi
harleensinghfiras92Let, Track length = 100 and B is x unit behind A when A finishes first track
A = 100
B = 100-x
C = 100-2x
When, A = 300
DIstance travelled by C = 100-x or 100+100-x
i.e. A/C = 100/(100-2x) = 300/(100-x) or 300/(200-x)
i.e. 3(100-2x) = 100-x or 3(100-2x) = 200-x
i.e. 300-6x = 100-x or 300-6x = 200-x
i.e. 5x = 200 and x = 40 or 5x = 100 and x = 20
i.e. A/C = 100/20 or 100/60
i.e. A/C = 5/1 or 5/3
Only Option D gives A/C = 5/3
Answer: Option D
Bunuel : OA mentioned seems INCORRECT. Please check or post OE