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The figure above shows a path around a triangular piece of land. Mary

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The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 14 Oct 2015, 20:26
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The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 80%

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-15_0825.png
2015-10-15_0825.png [ 4.43 KiB | Viewed 7917 times ]
[Reveal] Spoiler: OA

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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 14 Oct 2015, 21:14
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Bunuel wrote:
Image
The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 80%

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-15_0825.png


PR = \(\sqrt{8^2+6^2} = 10\)

DIstance walked by Mary = 8+6 = 14

% Exceeded distance of Mary = (14-10)*100/10 = 40%

Answer: Option B
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 15 Oct 2015, 00:52
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.



The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 80%


The total distance Mary walked is 8+6=14 miles, while the distance Ted walked is 10 miles( by the Pythagorean theorem √(8^2 +6^2)=√(100)=10).
So Mary walked 4 miles more than Ted. That means Mary walked 40%((4/10)*100) more walked than Ted. So the answer is (B).
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 17 Nov 2016, 08:36
Bunuel wrote:
Image
The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 80%

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-15_0825.png

The standard measurement of 90 degree scale is 3-4-5
So, if we multiply the measurement by 2 then I’ll get it as 6-8-10.
That means, PQ=10,
So, Ted’s walk distance is 10.
Distance walked by Mary = 8+6 = 14.
So Mary walked 4 miles more than Ted. If I want to make 100% of Mary’s walk, I have to multiply it by 10. Simultaneously, Ted’s walk will be 4*10=40%. So the answer is (B)
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 30 May 2017, 15:13
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Attached is a visual that should help.
Attachments

Screen Shot 2017-05-30 at 4.07.21 PM.png
Screen Shot 2017-05-30 at 4.07.21 PM.png [ 133.22 KiB | Viewed 2637 times ]


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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]

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New post 10 Dec 2017, 13:29
ANSWER SIMPLE:
Area = 1/2 bh
Area = 1/2 8*6
Area = 1/2 48
Area = 24

24 - 8 - 6 = distance Ted walked PR =10

Mary = 14
Ted = 10

Difference 4
Percentage difference 4/10
40%

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Re: The figure above shows a path around a triangular piece of land. Mary   [#permalink] 10 Dec 2017, 13:29
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