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# A cyclist travels the length of a bike path that is 225 miles long, ro

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

hi...how do we reach the final answer between A and C via this approach? since the other method is calculation intensive and time consuming...please help me out
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Re: A cyclist travels the length of a bike path that is 225 miles long, ro [#permalink]
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applebear wrote:
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.

hi...how do we reach the final answer between A and C via this approach? since the other method is calculation intensive and time consuming...please help me out

Hello

I think after eliminating the other answer choices as Bunuel suggested, we have to do the calculation anyway. But probably you can save some time by calculating only one of the limits (either upper limit or lower limit). So if you find that the minimum speed must be around 224.5/5.5, option A also gets eliminated and you are left with option C only.
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Re: A cyclist travels the length of a bike path that is 225 miles long, ro [#permalink]
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Re: A cyclist travels the length of a bike path that is 225 miles long, ro [#permalink]
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