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by adthedaddy » Sun Aug 26, 2012 2:58 am
This is from MGMAT book-3. I am not able to understand the solution. Experts please help with a simpler and an understandable solution.

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 hours, rounded to the nearest hour, then his average speed
must be between:
(A) 38 and 50 miles per hour
(C) 40 and 51 miles per hour
(E) 41 and 51 miles per hour
(B) 40 and 50 miles per hour
(D) 41 and 50 miles per hour

Ans: (C)
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by neelgandham » Sun Aug 26, 2012 5:22 am
I am not an expert but I will try my best to solve the question.

A cyclist travels the length of a bike path that is 225 Miles long, rounded to the nearest mile.
So the distance(say D) lies between 224.5(included) and 225.5(excluded).

i.e. 224.5<D<225.5

Time taken for the trip = T = 5hours, rounded to the nearest hour. So, the time lies between 4.5(Included) and 5.5(Excluded).

i.e. 4.5<T<5.5

Speed = S = Distance/Time.
So the minimum speed barrier is 224.5/5.5 and
the maximum speed barrier is 225.5/4.5
So, 224.5/5.5<S<225.5/4.5
i.e. 40.8 < S < 50.1111

(A) 38 and 50 miles per hour - If the speed is 50.11 then it doesn't lie between 38 and 50.So, A is an incorrect option.
(C) 40 and 51 miles per hour - CORRECT ANSWER
(E) 41 and 51 miles per hour - If the speed is 40.9 then it doesn't lie between 41 and 51.So, E is an incorrect option.
(B) 40 and 50 miles per hour - If the speed is 50.11 then it doesn't lie between 40 and 50.So, B is an incorrect option.
(D) 41 and 50 miles per hour - If the speed is 50.11 then it doesn't lie between 38 and 50.So, D is an incorrect option.

p.s: May I know the reason behind jumbling the answer choices? Trap eh ? :-)
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by adthedaddy » Sun Aug 26, 2012 5:37 am
p.s: May I know the reason behind jumbling the answer choices? Trap eh ?
Thanks Anil.
The jumble was only a typo... No traps for sure :)
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by neelgandham » Sun Aug 26, 2012 5:38 am
Ha Ha Ha! Just kidding mate.
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