Manhattan Quant Guides

chaitanya.mehrotra wrote:Doubt: How come we have taken 225.5 miles ? If round this it will become 226 thus max it can be 225.4 .
Similarly how come we have taken 5.5 hours ?If round this it will become 6 thus max hours could be 5.4 .

That is because if traveled path is 225 miles, rounded to the nearest mile, then he has traveled a distance which is larger than or equal to 224.5 miles and smaller than 225.5 miles. Note that in the opening end it is 'larger than or equal to' but in the closing end it is 'smaller than'. That is because in the closing end we can't fix a value for the actual distance traveled. It can be 225.499 miles or 225.499999999 miles or 225.49999....(infinite number of 9's) miles.

Hence, the proper way to bound the actual distance traveled (d) is 224.5 ≤ d < 225.5
And, similarly the proper way to bound the actual time taken (t) is 4.5 ≤ t < 5.5

Hence, his average speed (v) must be between (smallest distance)/(largest time) and (largest distance)/(smallest time).

Hence, (224.5/5.5) < v < (225.5/4.5) ---> 40.8 < v < 50.1 ---> 40 < v < 51

The correct answer is C.