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# A cyclist travels the length of a bike path that is 225

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A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Feb 2012, 10:51
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Difficulty:

95% (hard)

Question Stats:

29% (01:39) correct 71% (01:55) wrong based on 1100 sessions

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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

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!!
[Reveal] Spoiler: OA

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07 Feb 2012, 11:06
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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).

Hope it's clear.
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Feb 2012, 11:18
Thank you Bunuel,
Got your point that "the average speed must be between" implies "MUST cover all possible values"
All clear
Cheers!

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Feb 2012, 11:26
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supratim7 wrote:
Thank you Bunuel,
Got your point that "the average speed must be between" implies "MUST cover all possible values"
All clear
Cheers!

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.
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Feb 2012, 11:32
Oh yes.. Thank you again for the clear explanation.
Cheers!

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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21 Apr 2012, 11:33

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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24 Apr 2012, 10:19
Thank you. I also got D but now I understand why it's C. Best

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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27 Jun 2013, 02:25
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Aug 2013, 13:53
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:

Length is between 224.5 and 225.4 miles.
Trip is between 4:30 and 5:29 long

We want to maximize and minimize results.

225.4/4.5 = 50.1
224.5/5.5 = 40.8

40.8 <= R <= 50.1

So the range is greater than or equal to 40.8 and less than or equal to 50.1. the only answer choice that allows for all possible values of R is C.

ANSWER: C. 40 and 51 mph

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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24 Sep 2013, 11:51
Bunuel wrote:
supratim7 wrote:
Thank you Bunuel,
Got your point that "the average speed must be between" implies "MUST cover all possible values"
All clear
Cheers!

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.

Bunuel, You are Awesome!

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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26 Sep 2013, 07:35
is this a 700-difficulty question?!! I don't think so
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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26 Sep 2013, 08:19
Aldossari wrote:
is this a 700-difficulty question?!! I don't think so

Look at the stats: 72% of the users answered it incorrectly, so yes, it's 700-level question.
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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26 Sep 2013, 08:30
Bunuel wrote:
Aldossari wrote:
is this a 700-difficulty question?!! I don't think so

Look at the stats: 72% of the users answered it incorrectly, so yes, it's 700-level question.

is this how it works?

I thought the questions are more precisely rated rather than just looking at number of corrects and incorrects
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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26 Sep 2013, 08:38
Aldossari wrote:
Bunuel wrote:
Aldossari wrote:
is this a 700-difficulty question?!! I don't think so

Look at the stats: 72% of the users answered it incorrectly, so yes, it's 700-level question.

is this how it works?

I thought the questions are more precisely rated rather than just looking at number of corrects and incorrects

This a good way to rate. Moreover I also think that it's a 700 level question.
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Oct 2013, 08:44
When choosing ranges, Why cant have as following?

224.5 - 225 - 225.4
4.5 - 5 - 5.4

In my view, 225.5 is wrong as it is equally closer to 226.0, similarly 5.5 is equally closer to 6.
More so when we say rounded off to nearest, should we not adhere to rounding off principles?

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Oct 2013, 10:01
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ygdrasil24 wrote:
When choosing ranges, Why cant have as following?

224.5 - 225 - 225.4
4.5 - 5 - 5.4

In my view, 225.5 is wrong as it is equally closer to 226.0, similarly 5.5 is equally closer to 6.
More so when we say rounded off to nearest, should we not adhere to rounding off principles?

What do the dashes there represent?

Length of a path is 225 miles long, rounded to the nearest mile --> $$224.5\leq{distance}<225.5$$ --> any number from this range rounded to the nearest integer is 225 (notice strict inequality with 225.5: <).
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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Oct 2013, 10:46
Bunuel wrote:
ygdrasil24 wrote:
When choosing ranges, Why cant have as following?

224.5 - 225 - 225.4
4.5 - 5 - 5.4

In my view, 225.5 is wrong as it is equally closer to 226.0, similarly 5.5 is equally closer to 6.
More so when we say rounded off to nearest, should we not adhere to rounding off principles?

What do the dashes there represent?
>> dashes are supposed to represent range.

Length of a path is 225 miles long, rounded to the nearest mile --> $$224.5\leq{distance}<225.5$$ --> any number from this range rounded to the nearest integer is 225 (notice strict inequality with 225.5: <).

I got the point here, I took values as 225.4 , thereby missing on values on 225.40 to 225.49. I took 225.4 and got the wrong number.
Thanks for the help

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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19 Jul 2014, 00:03
calculation intensive question. I hope GMAT does not dish me anything calculation heavy

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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19 Jul 2015, 11:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A cyclist travels the length of a bike path that is 225 [#permalink]

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07 Aug 2015, 04:21
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!!

the cyclist travels in the range 224.5 - 225.4
time taken is in the range 4 hrs 31 m - 5 hrs 29 m
therefore, the average speed is in the range (224.5/5 hrs 29 m) - (225.4/4 hrs 31 m)
that means the range is 40.9 m/hr - 49.9 m/hr
rounded to 41 m/hr - 50 m/hr
the correct option is (D)

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Re: A cyclist travels the length of a bike path that is 225   [#permalink] 07 Aug 2015, 04:21

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