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Sam is training for the marathon. He drove 12 miles from his

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Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post Updated on: 12 Mar 2019, 09:55
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Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?

A. 1 ≤ n ≤23
B. 3 ≤ n ≤21
C. 5 ≤ n ≤19
D. 6 ≤ n ≤18
E. 9 ≤ n ≤15

Source: Mcgraw-Hill's GMAT

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Originally posted by Asifpirlo on 21 Aug 2013, 18:15.
Last edited by SajjadAhmad on 12 Mar 2019, 09:55, edited 2 times in total.
Edited the question.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 22 Aug 2013, 04:37
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Asifpirlo wrote:
Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?

A. 1 ≤ n ≤23
B. 3 ≤ n ≤21
C. 5 ≤ n ≤19
D. 6 ≤ n ≤18
E. 9 ≤ n ≤15


Consider the diagram below:
Attachment:
Distance2.png
Distance2.png [ 4.95 KiB | Viewed 3018 times ]

The length of any side of a triangle must be larger than the positive difference of the other two sides:

So, (12-4)<x<(12+4) --> 8<x<16.

So, (8-3)≤n≤(16+3) --> 5≤n≤19 (we use ≤ in case is along the straight line x).

Answer: C.

Hope it's clear.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 21 Aug 2013, 20:12
Asifpirlo wrote:
Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
A. 1 ≤n ≤23
B. 3 ≤n ≤21
C. 5 ≤n ≤19
D. 6 ≤n ≤18
E. 9 ≤n ≤15


Honestly, I just assumed this was all in a straight direct line away from Sam's home. So 12 + 6 -2 + 3 = 19 as the upper bound, and C is the only choice that fits this.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 19 Nov 2013, 23:38
Buneul, please explain the third line of your solution more elaborately.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 19 Nov 2013, 23:44
Buneul, when we get 8<x<16 we take all values between 8 and 16 excluding 8 and 16. How come you are considering them only in line 3 of your solution?
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 20 Nov 2013, 02:31
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 22 Nov 2013, 10:19
ProleFeed13 wrote:
Asifpirlo wrote:
Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
A. 1 ≤n ≤23
B. 3 ≤n ≤21
C. 5 ≤n ≤19
D. 6 ≤n ≤18
E. 9 ≤n ≤15


Honestly, I just assumed this was all in a straight direct line away from Sam's home. So 12 + 6 -2 + 3 = 19 as the upper bound, and C is the only choice that fits this.


I did the same but on the lower limit. If you think about it, it is correct approach because, the farthest that Red Rock can exist from his home is when he ran 6 miles from grey hill in exactly opposite direction of the home. so Red Rock will be 18 miles from home. And the max of the required range will be when he runs 3 miles in the opposite direction again after he retraced 2 miles back. this gives 18-2+3 = 19 miles as upper limit.

Likewise to get lower limit of the range, Red rock must be closest to his home which is 12-6 = 6 miles. he retraces 2 miles away to 8 miles and turns around and goes back 3 miles giving distance of 5 miles from home as lower limit.

took little over 2 mins for this.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 12 Jan 2015, 01:51
I don't know whether my method of reasoning is right...

but here it goes -------

Driven = 12 miles
Ran = 6 miles
As he retraced his path back for 2 miles ------ so subtract 2 from 6 --------

Ran again for 3 miles...

Maximum distance will be a straight line from his home to destination.....
Please check the figure attached for better understanding....

hence maximum distance would be 12 + 6 - 2 + 3 = 19

only option C has the same.
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 14 Jan 2015, 02:26
Values given in option C are the subset of option A & option B

Should the question be "what is the range of nearest possible values for n?"?
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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New post 30 Aug 2016, 07:09
ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+3=19 for the maximum, and 12-6+2-3=5 for the minimum, so C is the answer
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Re: Sam is training for the marathon. He drove 12 miles from his  [#permalink]

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Re: Sam is training for the marathon. He drove 12 miles from his   [#permalink] 25 Aug 2018, 02:20
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