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07 Feb 2012, 10:51
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:26) correct
72%
(02:39)
wrong
based on 2195
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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
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!!
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!!
07 Feb 2012, 11:06
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supratim7
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 --> \(4.5\leq{time}<5.5\);
Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator);
Lowest 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.
07 Feb 2012, 11:26
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supratim7
Alternative approach. It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.
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
Notice that since the range from A covers entire range from B and D, then B and D are out (if B or D is correct so is A and we can not have two correct answer, leave the bigger range). Similarly since the range from C covers entire range from E, then E is out too (if E is correct so is C and we can not have two correct answer, leave the bigger range).
Thus we are left only with two answer choices A (38, 50) and C (40, 51). From here it's much easier to get the correct answer.
Hope it's clear.
