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Paul drove 50 miles north, then changed direction and drove 120 miles

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Bunuel
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Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 04:37
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Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

A. 70 miles
B. 110 miles
C. 130 miles
D. 150 miles
E. 170 miles

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C
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Divyadisha
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 05:17
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Answer is C

x= {(120)^2 + (5)^2}^1/2

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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 07:49
Bunuel wrote:
Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

A. 70 miles
B. 110 miles
C. 130 miles
D. 150 miles
E. 170 miles

Kudos for a correct solution.


Using Pythagoras theorem,

Distance from the starting point= \sqrt{50^2+120^2}=130 miles
Answer D
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Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 08:39
Bunuel wrote:
Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

A. 70 miles
B. 110 miles
C. 130 miles
D. 150 miles
E. 170 miles

Kudos for a correct solution.



|---------120-------
|
|
150
|
|

Apply Pythagorus Theorem

\(\sqrt{(150^2+120^2}\)
\(\sqrt{2500+14400}\)
\(\sqrt{16900}\)
=130

Answer: C
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 12:48
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We can quickly see that the right triangle formed is one of the familiar Pythagorean triples:

50:120:X = 5(10):12(10):X

The triple that corresponds here is of course 5:12:13, so X = 13(10) = 130.

It is quite helpful to memorize the following triples:
3:4:5
5:12:13
7:24:25
8:15:17
9:40:41
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Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 13:22
If we make a diagram, it will be a right angled triangle with one side as 50 and the other side as 120.

We have to find the hypotenuse of this right angled triangle = \(\sqrt{50^2 +70^2}\) =130

Answer C
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   15 Apr 2015, 14:46
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So this forms a right angle triangle with base = 50 and perpendicular = 120
Hyp = sqroot(50x50+120x120)
Hyp = 130
Answer C
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   17 Apr 2015, 05:00
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Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

A. 70 miles
B. 110 miles
C. 130 miles
D. 150 miles
E. 170 miles

50 north, 120 east

5 - 12 - 13 triangle

130 C.
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   20 Apr 2015, 06:14
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Bunuel wrote:
Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

A. 70 miles
B. 110 miles
C. 130 miles
D. 150 miles
E. 170 miles

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION

Essentially, Paul drove along the legs of a big right triangle, and the hypotenuse is how far he is from his starting point.
Attachment:
pythagorean4.jpg
pythagorean4.jpg [ 6.18 KiB | Viewed 2676 times ]

Therefore, (distance from start)^2 = 50^2 + 120^2 = 2500 + 14400 = 16900

Distance from start = 16900^(1/2) = 130.

Answer: C.
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Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   08 Jun 2016, 02:41
The given problem is an application of pythagoras theorem
\(50^2\) + \(120^2\) = 2500 + 14400 = 16900
\(\sqrt{16900}\) = 130
So Paul is at a distance of 130 miles from his starting point

Correct Answer - C
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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink] New post   22 Jan 2021, 04:34
Instead using Pythagoras theorem use Pythagores triplets
Here for smallest odd no. 50~5 square it and then divide it by 2 》》 5~25~12.5~ 12 and 13 means 130

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Re: Paul drove 50 miles north, then changed direction and drove 120 miles [#permalink]
22 Jan 2021, 04:34
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