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Intern  Joined: 18 Sep 2011
Posts: 9
A cyclist travels the length of a bike path that is 225  [#permalink]

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46 00:00

Difficulty:   95% (hard)

Question Stats: 30% (02:31) correct 70% (02:42) wrong based on 1261 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!!
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: Inequalities PS  [#permalink]

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24
16
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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Intern  Joined: 18 Sep 2011
Posts: 9
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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1
Thank you Bunuel,
Got your point that "the average speed must be between" implies "MUST cover all possible values"
All clear Cheers!
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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25
5
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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Intern  Joined: 18 Sep 2011
Posts: 9
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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Oh yes.. Thank you again for the clear explanation.
Cheers!
Intern  Joined: 19 Sep 2011
Posts: 26
WE: Consulting (Consulting)
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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Thanks a lot bunuel.Your explanation made it very clear!
Intern  Joined: 21 Apr 2012
Posts: 2
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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Thank you. I also got D but now I understand why it's C. Best
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Distance/Rate Problems: distance-speed-time-word-problems-made-easy-87481.html

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
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Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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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:

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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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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is this a 700-difficulty question?!! I don't think so
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Math Expert V
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Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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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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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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You never fail until you stop trying ,,,
Math Expert V
Joined: 02 Sep 2009
Posts: 58411
Re: A cyclist travels the length of a bike path that is 225  [#permalink]

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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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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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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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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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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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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)
Intern  Joined: 20 May 2015
Posts: 2
A cyclist travels the length of a bike path that is 225  [#permalink]

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Bunuel wrote:
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.

Hi Thanks for your remarkable contribution to GMAT Aspirants.

I have one doubt here.Kindly help me.

Length of a path is 225 miles long, rounded to the nearest mile --> why we are not considering 224.5 ≤ distance ≤225.4
The trip took him 5 hrs, rounded to the nearest hour --> similarly what is wrong in considering 4.5≤ time ≤5.4

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. A cyclist travels the length of a bike path that is 225   [#permalink] 08 Aug 2015, 02:25

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