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Updated on: 01 Apr 2025, 06:43
Originally posted by MartyMurray on 05 Mar 2025, 17:39.
Last edited by MartyMurray on 01 Apr 2025, 06:43, edited 1 time in total.
Last edited by MartyMurray on 01 Apr 2025, 06:43, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
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Question Stats:
73% (01:52) correct
27%
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wrong
based on 224
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On a straight track, Arun and Sylvia started running in the same direction at the same time from the same end. Sylvia was faster than Arun, made it to the far end, turned back, and began running in the opposite direction before meeting Arun somewhere along the track. How long was the track?
(1) Sylvia ran twice as fast as Arun.
(2) Arun was 400 feet from the far end of the track when they met.
(1) Sylvia ran twice as fast as Arun.
(2) Arun was 400 feet from the far end of the track when they met.
15 Mar 2025, 07:57
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Given Information:
We are tasked with determining the length of the track.
Analyzing Statement (1): Sylvia ran twice as fast as Arun.
If Sylvia's speed is \( 2x \) and Arun's speed is \( x \), Sylvia completes the entire track and starts running back before meeting Arun. However, this statement alone does not provide any specific numerical information about the distance of the track.
Analyzing Statement (2): Arun was 400 feet from the far end of the track when they met.
This gives us a numerical piece of information, but it does not provide the relative speeds of Arun and Sylvia, which are necessary to determine how much of the track Sylvia covered before meeting Arun.
Combining Statements (1) and (2):
Now, we know:
Using their relative speeds, we can calculate how much distance each covered before meeting. Let the total length of the track be \( d \):
1. The time taken by Arun to cover \( d - 400 \) is equal to the time taken by Sylvia to cover \( d + (d - 400) \), since Sylvia reaches the end and starts running back.
We can now set up the relationship:
\(\text{Time taken by Arun} = \text{Time taken by Sylvia}\)
\(\frac{d - 400}{x} = \frac{d + (d - 400)}{2x}\)
Solve this equation to find \( d \). Combining the statements allows us to find a unique value for the track's length.
Conclusion for Statements (1) and (2) TOGETHER: SUFFICIENT.
Final Answer:
C. BOTH statements TOGETHER are sufficient, but neither alone is.
- Arun and Sylvia start at the same point, running in the same direction.
- Sylvia runs faster, reaches the far end, turns around, and then meets Arun while running back.
We are tasked with determining the length of the track.
Analyzing Statement (1): Sylvia ran twice as fast as Arun.
If Sylvia's speed is \( 2x \) and Arun's speed is \( x \), Sylvia completes the entire track and starts running back before meeting Arun. However, this statement alone does not provide any specific numerical information about the distance of the track.
- Conclusion for Statement (1): NOT sufficient.
Analyzing Statement (2): Arun was 400 feet from the far end of the track when they met.
This gives us a numerical piece of information, but it does not provide the relative speeds of Arun and Sylvia, which are necessary to determine how much of the track Sylvia covered before meeting Arun.
- Conclusion for Statement (2): NOT sufficient.
Combining Statements (1) and (2):
Now, we know:
- Sylvia runs twice as fast as Arun (\( 2x \) vs \( x \)).
- Arun is 400 feet from the far end of the track when they meet.
Using their relative speeds, we can calculate how much distance each covered before meeting. Let the total length of the track be \( d \):
1. The time taken by Arun to cover \( d - 400 \) is equal to the time taken by Sylvia to cover \( d + (d - 400) \), since Sylvia reaches the end and starts running back.
We can now set up the relationship:
\(\text{Time taken by Arun} = \text{Time taken by Sylvia}\)
\(\frac{d - 400}{x} = \frac{d + (d - 400)}{2x}\)
Solve this equation to find \( d \). Combining the statements allows us to find a unique value for the track's length.
Conclusion for Statements (1) and (2) TOGETHER: SUFFICIENT.
Final Answer:
C. BOTH statements TOGETHER are sufficient, but neither alone is.
08 Apr 2025, 03:01
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Sylvia should have run l plus 400 bot 2l minus 400 when meeting the other guy how could he have run more than twice his distance at twice the speed.
