Bunuel wrote:
mridulparashar1 wrote:
Bunuel wrote:
A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:
A. 38 and 50 mph
B. 40 and 50 mph
C. 40 and 51 mph
D. 41 and 50 mph
E. 41 and 51 mph
Length of a path is 225 miles long, rounded to the nearest mile --> 224.5\leq{distance}<225.5;
The trip took him 5 hrs, rounded to the nearest hour --> 4.5\leq{time}<5.5;
Lowest average rate is \frac{224.5}{5.5}\approx{40.8} (take the lowest value of nominator and highest value of denominator);
Highest average rate is \frac{225.5}{4.5}\approx{50.1} (take the highest value of nominator and lowest value of denominator);
40.8<rate<50.1.
Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: 40.8<rate<50.1. Only C does that: (40)<40.8<rate<50.1<(51). D can not be the answer as if rate=40.9 or if rate=50.01 then these possible values of the average rate are not covered by the range from this answer choice, which is (41-50).
Answer: C.
Hi Bunuel,
Refering to the rounding chapter in Number Theory examples
Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.
Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.
Shouldn't the range for distance be 224.5 < D< 225.4 ------> If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226.
Similarly for Time it should 4.5 <T< 5.4
Calculating Lowest Avg rate : 224.5/5.4 = 41.57
Highest : 225.4/4.5 = 50.08
The Answer remains C. Please confirm the range selection
Thanks
Should be as written. What about 225.499999? So, take 225.5 but exclude the endpoints, by writing < and > instead of <= and >=.
Hope it's clear.
Hi Bunuel,
Can you elaborate a bit more. I am not able to get the message.
Thanks