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A cyclist travels 20 miles at a speed of 15 miles per hour. If he returns along the same path, at what speed did he return?
(1) The cyclist took 2 hrs for the entire trip.
(2) The average speed for the round trip is 20 miles per hour.
The OA will be automatically revealed on Monday 31st of August 2026 07:00:06 PM Pacific Time Zone
(1) The cyclist took 2 hrs for the entire trip.
(2) The average speed for the round trip is 20 miles per hour.
The OA will be automatically revealed on Monday 31st of August 2026 07:00:06 PM Pacific Time Zone
31 Aug 2026, 02:35
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Given d = 20 miles one way, s = 15 m/hr, find speed while returning ( distance will be same as to and fro)
st 1 : total time = 2 hrs
find time taken to go from a to b
time = distance/speed , time= 20/15= 4/3 hrs
find time taken to come back from b to a
total time - time from a to b = 2-4/3= 2/3
speed from b to a = 20/(2/3) = 30 m/hr
st 1 is sufficient
st 2: average speed for round trip = 20m/hr
average speed = total distance/total time
total distance = 20+20 = 40 miles
20=40/total time
total time = 2 hrs
now is same as st 1, and we can find the speed while returning as done in st 1
hence st 2 is also sufficient
ANS D both statement are independently sufficient
Bunuel
st 1 : total time = 2 hrs
find time taken to go from a to b
time = distance/speed , time= 20/15= 4/3 hrs
find time taken to come back from b to a
total time - time from a to b = 2-4/3= 2/3
speed from b to a = 20/(2/3) = 30 m/hr
st 1 is sufficient
st 2: average speed for round trip = 20m/hr
average speed = total distance/total time
total distance = 20+20 = 40 miles
20=40/total time
total time = 2 hrs
now is same as st 1, and we can find the speed while returning as done in st 1
hence st 2 is also sufficient
ANS D both statement are independently sufficient
Bunuel
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31 Aug 2026, 04:30
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This is a Data Sufficiency question. Let's solve it step by step.
Given
t=2015=43 hourst=\frac{20}{15}=\frac43\text{ hours}
The total distance is:
20+20=40 miles20+20=40\text{ miles}
Statement (1): The cyclist took 2 hours for the entire trip.
Total time = 2 hours.
Time going:
43\frac43
Therefore, return time:
2−43=23 hours2-\frac43=\frac23\text{ hours}
Return speed:
v=202/3=30 mphv=\frac{20}{2/3}=30\text{ mph}
So Statement 1 alone is sufficient. ✅
Statement (2): Average speed for the round trip is 20 mph.
Remember:
Average speed=Total distanceTotal time\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}
So:
20=40Total time20=\frac{40}{\text{Total time}}
Therefore:
Total time=2 hours\text{Total time}=2\text{ hours}
And we already know that total time of 2 hours allows us to calculate the return speed:
v=30 mphv=30\text{ mph}
So Statement 2 alone is also sufficient. ✅
Answer
Since each statement independently gives us enough information:
D — Each statement alone is sufficient\boxed{\text{D — Each statement alone is sufficient}}
Key GMAT trick: Statement (2) gives you the total time because average speed is based on total distance ÷ total time, not the simple average of the two speeds.
Given
- Distance going = 20 miles
- Speed going = 15 mph
- Distance returning = 20 miles
- Return speed = vv, which we need to find.
t=2015=43 hourst=\frac{20}{15}=\frac43\text{ hours}
The total distance is:
20+20=40 miles20+20=40\text{ miles}
Statement (1): The cyclist took 2 hours for the entire trip.
Total time = 2 hours.
Time going:
43\frac43
Therefore, return time:
2−43=23 hours2-\frac43=\frac23\text{ hours}
Return speed:
v=202/3=30 mphv=\frac{20}{2/3}=30\text{ mph}
So Statement 1 alone is sufficient. ✅
Statement (2): Average speed for the round trip is 20 mph.
Remember:
Average speed=Total distanceTotal time\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}
So:
20=40Total time20=\frac{40}{\text{Total time}}
Therefore:
Total time=2 hours\text{Total time}=2\text{ hours}
And we already know that total time of 2 hours allows us to calculate the return speed:
v=30 mphv=30\text{ mph}
So Statement 2 alone is also sufficient. ✅
Answer
Since each statement independently gives us enough information:
D — Each statement alone is sufficient\boxed{\text{D — Each statement alone is sufficient}}
Key GMAT trick: Statement (2) gives you the total time because average speed is based on total distance ÷ total time, not the simple average of the two speeds.
