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Hi All,

This question doesn't actually require that much 'math' to solve, IF you recognize the logic behind what you "need" to know to answer the question.

We're asked for the length of time that it took to travel 5,000km (including 10 stopovers). To answer this question, we need to know the average speed during the 5,000km trip AND we need to know the length of each of the 10 stopovers.

1) The (i^th) stopover lasted (i^2) minutes.

This gives us a pattern for the length of each stopover:
The 1st stopover lasted 1^2 = 1 minute
The 2nd stopover lasted 2^2 = 4 minutes
The 3rd stopover lasted 3^2 = 9 minutes
Etc.
With this information, we can calculate the total amount of time spent on the stopovers, BUT we don't know how long it took to travel the 5,000km.
Fact 1 is INSUFFICIENT

2) The average speed between any two stopovers was 66km/hr.

Using the Distance Formula, we can calculate the travel time for the 5,000km....

D = (R)(T)
5,000 = (66)(T)
5,000/66 = T

With this information, we know how many hours it took to travel the 5,000km, BUT we don't know how long the stopovers were.
Fact 2 is INSUFFICIENT

Combined we know...
The length of the stopovers
The length to travel the 5,000km
So we CAN calculate the total time for everything.
Combined, SUFFICIENT

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total time in this case = travel time between two stopovers + time spent at each stopovers.

For the first stop over
Wait time (1)^2 = 1. Similarly, divide the entire journey into 10 stopovers. No need to calculate.
Travel time (From origin to Stop over point 1)

Repeat

Hence C. Both statements are necessary to find out the requested
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But we do not know the speed form starting point to first stopover roght?
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How long did Mr. X take to cover 5000 km journey with 10 stopovers?

(1) The (i^th) stopover lasted (i^2) minutes.

Since there are 10 stopovers, the stopover times are 1^2, 2^2, 3^2, ..., 10^2 minutes. So (1) gives the total stopover time, but not the driving time. Not sufficient.

(2) The average speed between any two stopovers was 66 kmph

Since the average speed between any two stopovers was 66 km/h, the average speed over the entire 5000 km of travel was 66 km/h. Thus, the travel time for the full journey can be determined, but the total stopover time is unknown. Not sufficient.

(1)+(2) Together, we know both the total stopover time and the travel time for the 5000 km journey. Sufficient.

Answer: C.

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