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A certain harbor has docking stations along its west and south docks,
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30 Jul 2018, 01:15
30 Jul 2018, 01:15
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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 [ 20.53 KiB | Viewed 42616 times ]
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Re: A certain harbor has docking stations along its west and south docks,
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10 Aug 2018, 18:55
10 Aug 2018, 18:55
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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
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!
Answer: B
Re: A certain harbor has docking stations along its west and south docks,
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19 Sep 2018, 00:55
19 Sep 2018, 00:55
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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
Restructuring the problem using coordinate plane we get
Docking in #2 : (0,3)
east of docking station #4 and directly north of docking station #7: (2,1)
Equation of this st. line is y=-x+3 [slope = -1]
so, the docking in X-axis Y=0, we get
0=-x+3, which is x = 3 (dock #8) [option b]
