Given: Assume the total distance to be 100x feet
1. Ryan swims 25x at full speed
2. Ryan swims (3/4)*75x = 56.25x at a reduced speed
3. Ryan swims 18.75x at full speed
Required: Average speed during the race.
This can be calculated if we have the total distance and the total time taken
Statement 1: Total distance = 100 feet
This does not tell us anything about the time.
Insufficient
Statement 2: Reduced speed = 1/3 of the full speed
Assume full speed = 3s
Reduced speed = s
Total distance = 100x
Total time taken = 25x/3s + 56.25x/s + 18.75x/3s
Average speed = 100x / (25x/3s + 56.25x/s + 18.75x/3s)
We cannot solve for average speed
Insufficient
Combining both the statements:
Average speed = 100 / (25/3s + 56.25/s + 18.75/3s)
Still we cannot calculate the average speed.
Insufficient
Option E
Question in the attachment
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Source: Beat The GMAT — Data Sufficiency |
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OptimusPrep
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Travelled at full speed are 1/4 of the total distance and then 1/4 of the remaining distance.
To determine the fraction traveled at full speed, let the total distance = 16 feet.
Initial distance traveled at full speed = (1/4)(16) = 4 feet.
Total remaining distance = 16-14 = 12 feet.
Remaining distance traveled at full speed = (1/4)(12) = 3 feet.
Total distance traveled at full speed = 4+3 = 7 feet.
Thus:
7/16 of the total distance is traveled at full speed, implying that 9/16 of the total distance is traveled at the lower speed.
Statements combined:
Case 1: full speed = 3 feet per hour, lower speed = 1 foot per hour
At 3 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/3.
At 1 foot per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/1 = (9/16)(100).
Total time = [(7/16)(100)]3 + (9/16)(100).
Case 2: full speed = 300 feet per hour, lower speed = 100 feet per hour
At 300 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/300 = (7/16)/3.
At 100 feet per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/100 = 9/16.
Total time = (7/16)/3 + 9/16.
Since the total time in Case 1 is different from the total time in Case 2, each case will yield a DIFFERENT AVERAGE SPEED.
Since the average speed for the whole race can be different values, INSUFFICIENT.
The correct answer is E.
To determine the fraction traveled at full speed, let the total distance = 16 feet.
Initial distance traveled at full speed = (1/4)(16) = 4 feet.
Total remaining distance = 16-14 = 12 feet.
Remaining distance traveled at full speed = (1/4)(12) = 3 feet.
Total distance traveled at full speed = 4+3 = 7 feet.
Thus:
7/16 of the total distance is traveled at full speed, implying that 9/16 of the total distance is traveled at the lower speed.
Statements combined:
Case 1: full speed = 3 feet per hour, lower speed = 1 foot per hour
At 3 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/3.
At 1 foot per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/1 = (9/16)(100).
Total time = [(7/16)(100)]3 + (9/16)(100).
Case 2: full speed = 300 feet per hour, lower speed = 100 feet per hour
At 300 feet per hour, the time to travel 7/16 of the 100 feet = d/r = [(7/16)(100)]/300 = (7/16)/3.
At 100 feet per hour, the time to travel 9/16 of the 100 feet = d/r = [(9/16)(100)]/100 = 9/16.
Total time = (7/16)/3 + 9/16.
Since the total time in Case 1 is different from the total time in Case 2, each case will yield a DIFFERENT AVERAGE SPEED.
Since the average speed for the whole race can be different values, INSUFFICIENT.
The correct answer is E.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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