Data Sufficiency

Mischa drove from A to B, a distance of 100 miles, at an average speed of 50 miles per hour, and then back from B to A along the same route at an average speed of m miles per hour. What is the value of m?

(1) Mischa's average speed for the entire round trip, excluding any time he spent at point B, was (m+50)/2 miles per hour.

(2) If Mischa's average speed from B to A had been 20% slower, the total time for the entire round trip, excluding any time Mischa spent at point B, would have been 12.5% greater.

Hi Rich,

Added the missing info. thanks for pointing out .

abhasjha wrote:Mischa drove from A to B, a distance of 100 miles, at an average speed of 50 miles per hour, and then back from B to A along the same route at an average speed of m miles per hour. What is the value of m?

(1) Mischa's average speed for the entire round trip, excluding any time he spent at point B, was (m+50)/2 miles per hour.

(2) If Mischa's average speed from B to A had been 20% slower, the total time for the entire round trip, excluding any time Mischa spent at point B, would have been 12.5% greater.

Question : What is the value of m which is the return speed?

Statement 1) Mischa's average speed for the entire round trip, excluding any time he spent at point B, was (m+50)/2 miles per hour.

Average Speed = Total Distance / Total Time

(m+50)/2 = (100+100) / [(100/50) + (100/m)]

Solving this we will get unique value of m therefore Sufficient

Statement 2) If Mischa's average speed from B to A had been 20% slower, the total time for the entire round trip, excluding any time Mischa spent at point B, would have been 12.5% greater

Total time of round trip with 20% slow speed from B to A = (100/50) + (100/0.8m)
Total time of round trip with Usual speed speed (m) from B to A = (100/50) + (100/m)

(112.5/100)[(100/50) + (100/m)] = [(100/50) + (100/0.8m)]

Solving this equation we will get a unique value of m therefore SUFFICIENT

Answer: Option D

IMPORTANT :

Solving an equation is not a mandatory exercise in Data Sufficiency Questions if you can make sure that the given equation will give you a unique value of Variable to be determined