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Two cars start off at the same point on a straight highway;

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Manager
Joined: 04 Jan 2013
Posts: 79

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Two cars start off at the same point on a straight highway; [#permalink]

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21 Mar 2013, 15:01
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Difficulty:

65% (hard)

Question Stats:

25% (01:11) correct 75% (01:27) wrong based on 20 sessions

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Two cars start off at the same point on a straight highway; each car travels in opposite direction to the other for 6km, and then takes an 8km travel after turning to the right. What is the shortest and longest distances that exist between them?

A. 12, 10
B. 11, 20
C. 20, 28
D. 14, 26
E. 20, 14
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2013, 15:03, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Two cars start off at the same point on a straight highway; [#permalink]

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21 Mar 2013, 15:31
How can A be the answer?

What is the shortest and longest distances that exist between them?
A. 12, 10
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Manager
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Re: Two cars start off at the same point on a straight highway; [#permalink]

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21 Mar 2013, 18:03
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Just draw the problem (see attached drawing) and do:

$$Z^2=6^2+8^2$$ ---> $$Z=10$$

I think Zarrolou is right, and the solution must be: (12, 20)

Shortest: 12
Longest: 20

Therefore, there is a mistake in the solutions provided because it says answer A is (12, 10)

Solution: (12, 20) --> see attached drawing

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Imagen1.jpg [ 9.71 KiB | Viewed 1261 times ]

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Manager
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Re: Two cars start off at the same point on a straight highway; [#permalink]

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21 Mar 2013, 18:10
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Kindly check the answer. It should be C.

The shortest distance will be along the hypotenuse and longest distance will be along the path taken by the two cars, i.e. along the other two sides of the triangles.
Image is attached.

Please give a kudo if you like my post.
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Re: Two cars start off at the same point on a straight highway; [#permalink]

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22 Mar 2013, 00:02
Abhii46 wrote:
Kindly check the answer. It should be C.

The shortest distance will be along the hypotenuse and longest distance will be along the path taken by the two cars, i.e. along the other two sides of the triangles.
Image is attached.

Please give a kudo if you like my post.

Pythagoras strikes again! Of course this is setting us up to have a right angle triangle, and a 3-4-5 (all values x2) triangle at that. The shortest distance will have to be 20 (10x2), but the longest distance is where this question falls apart. I'd say the longest distance between them is the path starting at point A, passing by Siberia, and then hitting point B.

This question sort of falls apart here but the shortest distance is nevertheless measurable and the longest distance can be measured with enough arbitrary rules (using only the roads that are used and not being able to take the same road twice, sort of thing). Using these completely realistic restrictions, the answer is C.

Hope this helps!
-Ron
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Re: Two cars start off at the same point on a straight highway;   [#permalink] 22 Mar 2013, 00:02
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