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# A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea

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Math Expert
Joined: 02 Sep 2009
Posts: 53069
A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea  [#permalink]

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05 Feb 2018, 05:46
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Difficulty:

15% (low)

Question Stats:

88% (01:36) correct 12% (02:13) wrong based on 46 sessions

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A girl at point X walks 1 mile east, then 2 miles north then 1 mile east, then 1 mile north, then 1 mile east, then 1 mile north to arrive at point Y. From point Y, what is the shortest distance to point X ?

(A) 7 miles
(B) 6 miles
(C) 5 miles
(D) 2.5 miles
(E) 1 mile

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Re: A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea  [#permalink]

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05 Feb 2018, 07:20
Bunuel wrote:
A girl at point X walks 1 mile east, then 2 miles north then 1 mile east, then 1 mile north, then 1 mile east, then 1 mile north to arrive at point Y. From point Y, what is the shortest distance to point X ?

(A) 7 miles
(B) 6 miles
(C) 5 miles
(D) 2.5 miles
(E) 1 mile

Total East distance = 3 miles (3 X 1 mile east)
Total North distance= 4 miles (2+1+1 north)

this is triangle with hyp as the shortest distance , so by Pythagorean triplets hyp= 5 miles

C
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A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea  [#permalink]

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05 Feb 2018, 07:21
Attachment:

From X to Y.png [ 1.96 KiB | Viewed 437 times ]

From the figure, we have the path the girl has taken to get from X to Y.
Since, the three triangles are right angled triangles, the sum of their
hypotenuse is the shortest distance to get from the point X to Y.

The hypotenuse of the right triangle with sides 1 and 2 is $$\sqrt{1+4} = \sqrt{5}$$

The hypotenuse of the other two isosceles right angles triangles(both sides = 1) is $$\sqrt{1+1} = \sqrt{2}$$

The shortest distance is $$\sqrt{5} + 2*\sqrt{2}= 2.2 + 2*1.4 = 5$$ (Option C)
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Re: A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea  [#permalink]

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06 Feb 2018, 17:30
Bunuel wrote:
A girl at point X walks 1 mile east, then 2 miles north then 1 mile east, then 1 mile north, then 1 mile east, then 1 mile north to arrive at point Y. From point Y, what is the shortest distance to point X ?

(A) 7 miles
(B) 6 miles
(C) 5 miles
(D) 2.5 miles
(E) 1 mile

We can depict the route from point X to point Y by the diagram above. We see that the shortest distance between X and Y is the dotted segment. Since the girl really travels 3 miles east and 4 miles north, we can create a right triangle such that the hypotenuse is the dotted segment and two legs are 3 and 4 (blue segments). Since this is a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse or by recognizing this triangle is a 3-4-5 right triangle. Therefore, we see that the shortest distance between X and Y is 5 miles.

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Re: A girl at point X walks 1 mile east, then 2 miles north then 1 mile ea   [#permalink] 06 Feb 2018, 17:30
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