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Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles

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Bunuel
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Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 03:13
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Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles
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B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 03:20
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Bunuel wrote:
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles

Kudos for a correct solution.


the displacement along east west direction=10-5=5..
the displacement along NS direction=3+9=12..
so we have a triangle with sides 5 and 12 and the dist between a and b is \(\sqrt{5^2+12^2}\)=13
ans B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 03:52
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Bunuel wrote:
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles

Kudos for a correct solution.


Draw the figure

Answer: option B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 05:02
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles

Solution -

If we draw the travel path, we can make 5 - 12 - x triangle.

x=13. ANS
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 08:25
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Bunuel wrote:
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles

Kudos for a correct solution.


Draw the path from Biker Bob on your scratch paper. Line segment AB will be the the longest segment of a 90-60-30 right triangle. The shortest side will be 5 (half of 10 miles west) while the height is 12 (3 north + 9 north).

So we have a 5 12 - X triangle... which tends to be a recycled 5 12 13 triangle.

Answer B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 08:58
drawing diagram it comes to pythagorus pair.
5-12-13

hence answer is B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 10:15
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A. 12 miles Not true. The sides are not equal.
B. 13 miles True. Triangle is 30-60-90, and 5-12-13 is one of them.
C. 15 miles Not true. \(15^{2} = 225\), and \(225 - 25 \neq{144}\).
D. 17 miles Not true. Must be less than the sum of the two other sides.
E. 19 miles Not true. Must be less than the sum of the two other sides.

B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   01 Jul 2015, 12:49
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Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles


Option B is correct

Using Pythagoras we have one side i,e total distance traveled in north direction = 9+3=12m
other being the base ie distance traveled west- distance traveled eat=10-5=5 m
now this third side or the distance between town A and Town B=12^2+ 5^2=sq root 169=13m
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   06 Jul 2015, 03:20
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Bunuel wrote:
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:


If you draw a rough sketch of the path Biker Bob takes, as shown to the right, you can see that the direct distance from A to B forms the hypotenuse of a right triangle. The short leg (horizontal) is 10 — 5 = 5 miles, and the long leg (vertical) is 9 + 3 = 12 miles. Therefore, you can use the Pythagorean Theorem to find the direct distance from A to B:

5^2 + 12^2 = c^2
25 + 144 = c^2
c^2 = 169
c = 13

You might recognize the common right triangle: 5-12-13. If so, you don’t need to use the Pythagorean theorem to calculate the value of 13

Answer: B.

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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   21 Sep 2020, 06:15
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Bunuel wrote:
Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5 miles east, and then 9 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)

A. 12 miles
B. 13 miles
C. 15 miles
D. 17 miles
E. 19 miles


Solution:

We see that Town B is 3 + 9 = 12 miles north and 10 - 5 = 5 miles west of Town A. Therefore, by the Pythagorean theorem, Town B is √(12^2 + 5^2) = √169 = 13 miles from Town A.

Answer: B
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink] New post   07 Jul 2022, 05:34
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Re: Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles [#permalink]
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