Two cyclists, Alex and Jordan, are cycling around a circular track.

Question

Two cyclists, Alex and Jordan, are cycling around a circular track. If they start at exactly the same time, in how many seconds will Alex have completed exactly one more lap than Jordan?

(1) Alex completes each lap in 20 seconds and Jordan completes each lap in 25 seconds.

(2) They start at the same point on the track and cycle in the same direction.

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Bunuel · Accepted Answer

Official Solution:

Two cyclists, Alex and Jordan, are cycling around a circular track. If they start at exactly the same time, in how many seconds will Alex have completed exactly one more lap than Jordan? 
 
(1) Alex completes each lap in 20 seconds and Jordan completes each lap in 25 seconds.
 
In every 25 seconds, Jordan completes 1 lap, while Alex completes 1.25 laps (1 lap plus 25% of the lap). So Alex gains 0.25 laps on Jordan every 25 seconds. To gain 1 full lap, Alex needs 4 such intervals: 25 * 4 = 100 seconds. Sufficient.
 
(2) They start at the same point on the track and cycle in the same direction.
 
This information is irrelevant. The starting point and direction do not affect the time it takes for one cyclist to complete exactly one more lap than the other. Not sufficient.

Answer: A

sachbash14 · Answer

1) Tells us how fast Alex and Jordan complete a lap, respectively; however, we do not know where they start relative to each other in the circular track. If they are starting at the same point, we have sufficient information, but if they are starting at different places on the track, we cannot say. Therefore, insufficient.

2) Alone, we do not know the rate at which they complete a lap on the track, therefore insufficient.

Therefore, answer choice (C).

2) Alone, we do not know the rate at which they complete a lap on the track, therefore insufficient.

Therefore, answer choice (C).

manoj2025 · Answer

IMO, the direction doesn't matter. No.of lapses matter and it's independent of each person. 20(x+1) = 25x. I think A itself works

ravi1522 · Answer

Hello,
Option 1 is sufficient 
As Alex will complete 1.25laps in 25 second ,so we can calculate the time at which he will take one lap extra

option 2
The direction is irrelevant

So option A is correct choice .

Thanks

gmatophobia · Answer

The distance covered by each cyclist is the perimeter of the circular track. Let's assume this distance = p meters

Statement 1

(1) Alex completes each lap in 20 seconds and Jordan completes each lap in 25 seconds.

Speed of Alex =  \frac{p}{20}  meters per second

Speed of Jordan =  \frac{p}{25}  meters per second

We can determine that Jordan is slow of the two, and the difference in speed =  \frac{p}{20} - \frac{p}{25}  =  \frac{5p}{20*25}

Time taken to complete one more lap =  \frac{p}{\frac{5p}{500}} = 100

Statement 1 alone is sufficient to answer the question.

Statement 2

(2) They start at the same point on the track and cycle in the same direction.

We need the difference in speed to find the time. Hence, this statement alone is not sufficient to answer the question asked.

Option A

aryanrgupta · Answer

Every second , Alex gains:

1/20−1/25 = (5−4)/100 = 1/100 laps per second

So in  100 seconds , Alex will be  1 lap ahead  of Jordan.

A sufficient, B is not sufficient

Two cyclists, Alex and Jordan, are cycling around a circular track.

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GMAT Data Sufficiency (DS) Questions

Two cyclists, Alex and Jordan, are cycling around a circular track.

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