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

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

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.

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]
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]

GMATinsight Bunuel niks18 chetan2u
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%

Quote:
PR = $$\sqrt{8^2+6^2} = 10$$

DIstance walked by Mary = 8+6 = 14

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

Can experts suggest why we took 10 in denominator and not 14?
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
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GMATinsight Bunuel niks18 chetan2u
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%

Quote:
PR = $$\sqrt{8^2+6^2} = 10$$

DIstance walked by Mary = 8+6 = 14

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

Can experts suggest why we took 10 in denominator and not 14?

% will be (extra distance walked by Mary)/(Distance walked by Ted)

We need a % over distance walked by Ted,
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
We're told that 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 and Ted walked directly from P to R. We're asked by what PERCENT the distance that Mary walked exceeded the distance that Ted walked. This question is based around Geometry patterns and the Percent Change Formula.
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
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Formula to be used:

Pythagoras theorem: $$Hypotenuse^2$$ = $$Base^2$$ + $$Perpendicular^2$$

Total distance walked by Mary = $$PQ + QR = 8 + 6 = 14 miles$$

Total distance walked by Ted = PR

Applying Pythagoras theorem in the Triangle PQR:

$$PR^2$$ = $$PQ^2$$ + $$QR^2$$

$$PR^2$$ = $$8^2$$ + $$6^2$$ $$= 64 + 36 = 100$$

PR = +10 OR -10

Since PR is a distance and cannot be negative, PR = 10 miles

The difference in the distance walked by Mary and Ted = 14 - 10 = 4 miles

Percent of the distance that Mary walked more than Ted walked = $$\frac{4}{10}$$ * 100 = 40%

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

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.

Attachment:
2015-10-15_0825.png

Since we have a right triangle, we see that we have a 6-8-10 right triangle.

Mary’s distance was 14, and Ted’s distance was 10, so Mary traveled 4 miles more than Ted.

4/10 = 40%

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

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.

Attachment:
2015-10-15_0825.png

First, the real amount of time that this question should take us. 8 and 6,

that means that this is a 10, and this is a 14. 14 exceeds 10 by 4,

out of the original number which is a 10, that is 40%, that's it! The correct

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

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.

Attachment:
2015-10-15_0825.png

Use Puythagorean Triples form, $$PR = 10$$

Distance covered by Mary is $$8 + 6 = 14$$ ; Distance covered by Tom is $$10$$

Quote:
what percent did the distance that Mary walked exceed the distance that Ted walked?

$$= \frac{4}{10}*100 = 40$$ , Answer must be (B)
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
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Re: The figure above shows a path around a triangular piece of land. Mary [#permalink]
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