supratim7 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

My interpretation is as follows,

224.5 ≤ distance < 225.5

4.5 ≤ time < 5.5

so, rate must be between 40.81 (224.5/5.5) and 50.11 (225.5/4.5)

OR 40.81 < rate < 50.11

My question: Why C) 40 and 51 mph is the OA ??

The rate cant be, for example, 40.5 or 50.5

Shouldn't the answer be D) 41 and 50 mph ?? Since ALL possible vales between 41 & 50 will satisfy the equation.

Pls help..

Cheers!!

Hi and welcome to GMAT Club. Below is a solution for the question.

It can be done in another way but since you chose algebraic approach I'll proceed with it

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 \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator);

Highest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest 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.

Hope it's clear.

Hi Thanks for your remarkable contribution to GMAT Aspirants.

I have one doubt here.Kindly help me.

lowest average speed=shortest possible distance/maximum possible time=(224.5 miles)/(5.4 hr) =41.57 miles/hr

which is not included in any of the options.What I am doing wrong with this thought process.