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An airplane was due north of a tropical island when hurricane warning

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An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 17 Oct 2016, 05:57
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A
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E

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  95% (hard)

Question Stats:

34% (01:50) correct 66% (01:40) wrong based on 102 sessions

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An airplane was due north of a tropical island when hurricane warning arrived at noon. In what direction was the tropical island from the position of the airplane at 3 pm?

(1) To circumvent the path of the hurricane, the airplane flew due west at 200 miles per hour from noon till 2 pm, and from 2 pm until 3 pm, it flew due south at 300 miles per hour.

(2) At 3 pm, the airplane was exactly 450 miles from the tropical island.

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An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post Updated on: 12 Jul 2017, 10:45
stat 1 : the route travelled forms a right triangle with hypotenuse 500m due southwest if the plane starts from the island,, what is the initial position of the plane is different..
insuff

stat 2 : clearly insuff
hence E

Originally posted by mohshu on 17 Oct 2016, 11:02.
Last edited by mohshu on 12 Jul 2017, 10:45, edited 1 time in total.
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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 17 Oct 2016, 18:25
statement 1: island can be in east or south east direction.

Insufficient

Statement 2:

Insufficient

Statement 1&2:

If the island is at east, then the distance between plane and island should be 400 miles.

So the island is at south east direction from plane at a distance of 450 miles.

C





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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 11 Jul 2017, 14:56
1
Wow, no correct answers on this one yet.

I got E as the Island can be anywhere south of the airplane to start; we need to know what distance the island is from the airplane.

For example:
(1) If it is very close to the airplane, the airplane will finish south west of the island.
(2) If the island initially is 300 miles south, the airplane will finish directly west of the island.
(3) If the island is beyond 300 miles south, the airplane will be north west of the island.
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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 12 Jul 2017, 01:13
I agree with Laxpro.
The answer is completely dependent on the initial position of the plane. Even if the plane is straight north of the island at the beginning, at 3pm, it could be NW or SW of the island :

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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 12 Jul 2017, 03:19
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Bunuel wrote:
An airplane was due north of a tropical island when hurricane warning arrived at noon. In what direction was the tropical island from the position of the airplane at 3 pm?

(1) To circumvent the path of the hurricane, the airplane flew due west at 200 miles per hour from noon till 2 pm, and from 2 pm until 3 pm, it flew due south at 300 miles per hour.

(2) At 3 pm, the airplane was exactly 450 miles from the tropical island.


I used coordinate geometry to solve this question.
Since I cannot draw here, please bear with me. I will try and explain my process.

At 12 pm - Plane is due north of the island, so if the island is at coordinate (0,0), then the plane is at (0,y).
Storm warning. Where is the plane relative to the island at 3pm? Or what are the coordinates?

1) Plane flew west from (0,y) at 200 miles per hour till 2 pm
Plane's new position is (-400,y)
Plane flew south from (-400,y) at 300 miles per hour for 1 hour.
Plane's new position is (-400,y-300)
y=?
Insufficient.

2) At 3 pm the plane is 450 miles from the island
It should be in any direction. Insufficient.

(1+2)
Plane's last known position is (-400, y-300)
The distance is 450 miles from the island.

If y > 300 then it's above the x-axis and if y < 300 then it's below the x-axis.
Insufficient.

Answer is E.
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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 12 Jul 2017, 03:52
Let the Distance between plane and tropical Island be X.
We know that the plane is in the north to the tropical Island.And we have to find out the direction the plane would be at 3 O'clock.

So by 1)
So by this the plane 200 miles west and 300 miles south.
But we don't know the original distance between plane and tropical Island. Considering this the plane could be in North West or in South West.

By 2)
The distance between plane and tropical Island doesn't guide to know the direction of plance.

Combining 1) and 2)
After we know the distance between plane and tropical Island and we know that it could be in North west and South West

So option E is correct.

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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 12 Jul 2017, 11:12
I got the answer C because if it's due north, I was thinking that it is somewhere on the y-axis north. Not NE or NW. Then if we know both the distance it was flying from 12-3 and the relative orientation in space plus the final distance to the island, we can figure out exactly where it began its journey on the y-axis and hence where final position was.

Am I missing something?
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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 12 Jul 2017, 11:18
Nagge wrote:
I got the answer C because if it's due north, I was thinking that it is somewhere on the y-axis north. Not NE or NW. Then if we know both the distance it was flying from 12-3 and the relative orientation in space plus the final distance to the island, we can figure out exactly where it began its journey on the y-axis and hence where final position was.

Am I missing something?


I failed to consider that the plane could have started close to the island and gone around it (negative y axis). There is therefore two possible answers... answer E is correct
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Re: An airplane was due north of a tropical island when hurricane warning  [#permalink]

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New post 22 Jul 2018, 04:15
Bunuel wrote:
An airplane was due north of a tropical island when hurricane warning arrived at noon. In what direction was the tropical island from the position of the airplane at 3 pm?

(1) To circumvent the path of the hurricane, the airplane flew due west at 200 miles per hour from noon till 2 pm, and from 2 pm until 3 pm, it flew due south at 300 miles per hour.

(2) At 3 pm, the airplane was exactly 450 miles from the tropical island.


Statements combined:
Image
The dotted green line indicates the plane's position at 12pm.
The blue right triangle indicates the plane's position at 3pm.
The two dotted red lines show positions for the island that are 450 miles from the plane's position at 3pm.
Since the island can be in different positions, the two statements combined are INSUFFICIENT.


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Re: An airplane was due north of a tropical island when hurricane warning &nbs [#permalink] 22 Jul 2018, 04:15
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