A and B are two runners competing in a race on a circular track of

Question

A and B are two runners competing in a race on a circular track of length L meters. They start at the same time from the same point and run in the same direction. A runs at a constant speed of S_A meters per second, while B runs at a constant speed of S_B meters per second, where S_A > S_B. If A laps B exactly once during the race, how long does the race last?

(1) A completes one full lap in 40 seconds.

(2) The difference between A’s and B’s speeds is 2.5 meters per second.

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Official Answer

E

(1) A completes one full lap in 40 seconds.

(2) The difference between A’s and B’s speeds is 2.5 meters per second.

f3rn4nd44m0r1m · Answer

To know how long does the race last we need to know the distance and the speed of A, because he finish earlier than B (he is faster and the distance is the same for both). 
Speed = distance / time

Okay, now we know the time A completes one lap, but not the total distance of the race or A's speed. Insufficient. Eliminate A and D.

Now we now the difference of speeds between A and B, but I have no clue about A's speed and race distance. Insufficient. Eliminate B

Together, they give me time of A (in one lap, not all race) and diference of speed between A and B, but no clue about A's speed again and total distance. Together they are insufficient. Eliminate C

Choose E

manish8242 · Answer

I did not get the question properly can you explain me this question in a naive way? I thought A completes one lap in 40 sec means the race is over in 40 sec. tell me where i am missing it.

f3rn4nd44m0r1m · Answer

A completing one lap in 40 seconds  ≠  the race ends in 40 seconds. The race could have multiple laps,which is probably true since A manages to lap B.

Considering (1) info, to calculate the total race time, we would need A’s speed, and for that we must know the  length of the lap . 
If statement (2) had given us this information, then together the statements would be sufficient (answer C). But since it does not, we cannot solve.
 
Example: 
 
 Suppose the track length is 400 meters. 
 If A completes one lap in 40 seconds, his speed is 400 ÷ 40 = 10 m/s. 
 If the race is 2 laps (800 m), the time is 80 seconds. 
 If the race is 5 laps (2000 m), the time is 200 seconds.

So, even with the time to complete 1 lap, without knowing the lap length (or the total distance) and A's speed, we cannot determine the race duration.
✅ Correct answer:  E  (neither statement alone nor both together are sufficient).

A and B are two runners competing in a race on a circular track of

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GMAT Data Sufficiency (DS) Questions

A and B are two runners competing in a race on a circular track of

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