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# Shane drives from his house to the beach by one of three possible rout

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Joined: 02 Sep 2009
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Shane drives from his house to the beach by one of three possible rout  [#permalink]

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09 Jan 2018, 23:42
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Difficulty:

55% (hard)

Question Stats:

50% (02:04) correct 50% (02:06) wrong based on 34 sessions

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Shane drives from his house to the beach by one of three possible routes, a, b, or c from shortest to longest. If he must return by one of these routes, what is the difference between the longest route and the shortest route?

(1) If he never takes the same route leaving and returning, the longest distance he travels is 48 miles for the entire trip.
(2) Taking route a to the beach and returning using route b, Shane travels a distance of 34 miles.

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Re: Shane drives from his house to the beach by one of three possible rout  [#permalink]

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10 Jan 2018, 00:40
Bunuel wrote:
Shane drives from his house to the beach by one of three possible routes, a, b, or c from shortest to longest. If he must return by one of these routes, what is the difference between the longest route and the shortest route?

(1) If he never takes the same route leaving and returning, the longest distance he travels is 48 miles for the entire trip.
(2) Taking route a to the beach and returning using route b, Shane travels a distance of 34 miles.

So a < b < c. We have to determine value of (c-a).

(1) If the onward and return routes are different, longest distance would be covered by taking routes 'b' and 'c'. So we are given that b+c = 48. But we dont know anything about 'a'. Insufficient.

(2) This gives us that a+b = 34. But nothing about c. Insufficient.

Combining the statements, subtracting the two equations; we get:
(b+c) - (a+b) = 48 - 34 OR c - a = 14. Sufficient.

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Re: Shane drives from his house to the beach by one of three possible rout  [#permalink]

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28 May 2019, 08:14
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Re: Shane drives from his house to the beach by one of three possible rout   [#permalink] 28 May 2019, 08:14
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