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

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

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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.
Spoiler: OA

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

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New post 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.

Hence C answer
Re: Shane drives from his house to the beach by one of three possible rout   [#permalink] 10 Jan 2018, 00:40
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