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A certain harbor has docking stations along its west and south docks,

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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

East of 4 and North of 7 means it has traveled TWO ( 2 to 4) steps down and TWO(5 to 7) steps east
But it has to travel 3 steps from 2 to 5, so it will travel 3 to the east = 5+3=8

ofcourse it can be done by finding slope but easier to assimilate this way

B
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Originally posted by chetan2u on 30 Jul 2018, 01:37.
Last edited by adkikani on 05 Apr 2020, 23:06, edited 1 time in total.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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Finding slope of line using two points
(5,2)- when the boat is docked on west harbour
(7,4) - given boat has passed through this point

then slope [(4-2)]/[(7-5)]=1

Then we can find the port where the boat is docked in the south harbour

1= [(4-5)]/[(7-s.port)]
7-s.port=-1
s.port=8
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
[quote="Bunuel"]
A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

The slope of the line is given by tan theta
At the instance when boat is at intersection of 4&7 tan theta=2/2
Now as slope is constant and y is 3 stations down from dock 2 (tan theta=3/3)....the destination dock has to be 3 stations to right of dock 5
Hence #8

Hit kudos if you like the answer!
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

Attachment:
shot19.jpg

Coordinates of #2 $$(0,3),$$ #4&7 $$(2,1)$$

The line is $$y=mx+b$$

$$m= \frac{(3-1)}{(0-2)} =-1$$
So,
$$y=-x+b$$

Now, when $$y=3$$

$$3=-1*0+b$$
$$b=3$$

So, the line intercept at $$3$$ or dock $$8$$ of the south dock.

Ans. B.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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chetansharma wrote:
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

East of 4 and North of 7 means it has traveled TWO ( 2 to 4) steps down and TWO(5 to 7) steps east
But it has to travel 3 steps from 2 to 5, so it will travel 3 to the east = 5+3=8

ofcourse it can be done by finding slope but easier to assimilate this way

B

This was the best explanation so far

Posted from my mobile device
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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Hey
Is it an absolutely terrible idea to solve this question without any math?
I just used the mouse pointer to draw an imaginary line from #2 to the coordinates of #7,#4 and it only makes sense that the boat will reach #8 if it's travelling on a straight path.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
ScottTargetTestPrep wrote:
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

Attachment:
shot19.jpg

Let’s rethink this problem as one that involves the equation of a line. Station 5 is the origin (0,0), and all other stations take on the traditional values on the x and y axes. Thus, when the boat leaves station #2, the ordered pair is (0,3), and the line of the boat’s path passes through the point (station #7, station #4), or (2,1). The line that connects these two points has a slope of (3 – 1)/0 – 2) = 2/-2 = -1. Using y = -1x + b, we substitute the values from (0,3), obtaining 3 = (-1)(0) + b, and so b = 3. Thus, the equation of the line connecting the two points is y = -x + 3.

We now plug in the ordered pairs of the answer choices to determine which of their equivalent ordered pairs satisfies the equation y = -x + 3.

Choice A: station #7 is at (2,0). Does 0 = -2 + 3? No.

Choice B: station #8 is at (3,0). Does 0 = -3 + 3? Yes!

ScottTargetTestPrep MartyTargetTestPrep

Thank you for this helpful explanation. How do you know thought that the graph is going up by the same increments on both axes? For instance, what if each dash on the x axis goes up in intervals by 2 and each dash on the y axis goes up by intervals of 3? How do you know that the graph is spread out even in constant increments at all (e.g., what if from point 6 to 7 was 3 and from points 7 to 8 was 4?) I was just confused how to interpret this graph overall given that there is no "key" if you will to understand if things are draw to scale/we can assume each dash represents 1 unit. Thanks again.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
woohoo921 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

Attachment:
shot19.jpg

Let’s rethink this problem as one that involves the equation of a line. Station 5 is the origin (0,0), and all other stations take on the traditional values on the x and y axes. Thus, when the boat leaves station #2, the ordered pair is (0,3), and the line of the boat’s path passes through the point (station #7, station #4), or (2,1). The line that connects these two points has a slope of (3 – 1)/0 – 2) = 2/-2 = -1. Using y = -1x + b, we substitute the values from (0,3), obtaining 3 = (-1)(0) + b, and so b = 3. Thus, the equation of the line connecting the two points is y = -x + 3.

We now plug in the ordered pairs of the answer choices to determine which of their equivalent ordered pairs satisfies the equation y = -x + 3.

Choice A: station #7 is at (2,0). Does 0 = -2 + 3? No.

Choice B: station #8 is at (3,0). Does 0 = -3 + 3? Yes!

ScottTargetTestPrep MartyTargetTestPrep

Thank you for this helpful explanation. How do you know thought that the graph is going up by the same increments on both axes? For instance, what if each dash on the x axis goes up in intervals by 2 and each dash on the y axis goes up by intervals of 3? How do you know that the graph is spread out even in constant increments at all (e.g., what if from point 6 to 7 was 3 and from points 7 to 8 was 4?) I was just confused how to interpret this graph overall given that there is no "key" if you will to understand if things are draw to scale/we can assume each dash represents 1 unit. Thanks again.

The question stem tells us that "any two adjacent docking stations are separated by a uniform distance d". The figure also shows this distance of d between the stations #1 and #2. So if the distance from #6 to #7 is 3, then the distance from #7 to #8 cannot be 4, it would go against the "uniform distance" condition given in the question stem. If the distance from #6 to #7 is 3, then the distance from #7 to #8, as well as the distances from #1 to #2, from #2 to #3, from #10 to #11 etc. must all be 3.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
chetan2u wrote:
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

East of 4 and North of 7 means it has traveled TWO ( 2 to 4) steps down and TWO(5 to 7) steps east
But it has to travel 3 steps from 2 to 5, so it will travel 3 to the east = 5+3=8

ofcourse it can be done by finding slope but easier to assimilate this way

B

Great explanation chetan2u
One question it travel 3 steps from 2 to 5 but why is it need to be travel 3 to the east? Could you help clarify ? Thanks
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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Kimberly77 wrote:
chetan2u wrote:
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

NEW question from GMAT® Quantitative Review 2019

(PS08375)

East of 4 and North of 7 means it has traveled TWO ( 2 to 4) steps down and TWO(5 to 7) steps east
But it has to travel 3 steps from 2 to 5, so it will travel 3 to the east = 5+3=8

ofcourse it can be done by finding slope but easier to assimilate this way

B

Great explanation chetan2u
One question it travel 3 steps from 2 to 5 but why is it need to be travel 3 to the east? Could you help clarify ? Thanks

From docking station 2, coordinates can be written as (5,2), it reaches (7,4), that is it moves 2 eastward as it moves 2 southwards. Thus one step down also means one step towards rought.

Now, the boat has to move down from 2 to 5, that is THREE steps down, so it should also mean THREE steps to right.
Thus 5+3 or 8.
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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As you mentioned "one step down also means one step towards right" , is this due to slope is -1?
Thanks
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
Kimberly77 wrote:
As you mentioned "one step down also means one step towards right" , is this due to slope is -1?
Thanks

Yes, absolutely correct. It is because of the slope
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
chetan2u wrote:
Kimberly77 wrote:
As you mentioned "one step down also means one step towards right" , is this due to slope is -1?
Thanks

Yes, absolutely correct. It is because of the slope

Great, thanks chetan2u for confirmation
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Re: A certain harbor has docking stations along its west and south docks, [#permalink]
Bunuel wrote:

A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?

A. #7
B. #8
C. #9
D. #10
E. #11

(PS08375)

Attachment:
shot19.jpg

­Hi
I just used my imagination as shown as the distance between them is same and the boat is travelling diagonally

would this approach be wrong?
Re: A certain harbor has docking stations along its west and south docks, [#permalink]
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