Bunuel wrote:
Brian drives a certain part of his journey at an average speed of 30 miles per hour and the rest at an average speed of 60 miles per hour. If he drives for 100 miles, is his average speed for the journey greater than 45 miles per hour?
(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.
(2) Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.
Question: ... is his average speed for the journey greater than 45 miles per hour?
For a moment let's assume that would the average speed = 45 mph
45 is the midpoint of 30 and 60, hence if Brain drives at 30 mph for the same duration as he drives at 45 mph, the average speed will be 45 mph.
The average speed will tend to shift towards 30 or 60 depending on the time interval Brain drives at each of the speeds. Put in other words, if Brain spends more time driving at 30 mph than he spends driving at 60 mph, the average speed will be less than 45mph. On the contrary, if Brain spends more time driving at 60 mph than he spends driving at 30 mph, the average speed will be more than 45mph.
In a nutshell, we want to find the time Brain drove at either 30 mph or 60 mph.
Statement 1(1) Brian drives for 30 miles per hour for twice the time than he drives for 60 miles per hour.
This statement tells us Brain spend more time driving at 45 mph than he spent driving at 60 mph. Hence the average speed will be less than 45 mph.
The statement is sufficient to answer a definite No to the target question "Is his average speed for the journey greater than 45 miles per hour"
We can eliminate B, C and E.
Statement 2Had Brian driven at an average speed of 40 miles per hour rather than 30 miles per hour, his average speed for the journey would have been 48 miles per hour.Had Brain spent equal time driving at 40mph and at 60mph the average speed would have been 50mph. However, we see that the average speed is on the lower end and has "shifted" towards 40 mph.
Hence, we can conclude that Brain spent more time driving at 40 mph than at 60 mph. As the time he drove at 40mph correlates to the time he drove at 30 mph, we can say that the average speed would be less than 45.
The statement is sufficient to answer a definite No to the target question "Is his average speed for the journey greater than 45 miles per hour"
Option D