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If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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30 Jul 2015, 10:20
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If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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30 Jul 2015, 10:32
Bunuel wrote: If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
A. 0 B. 1 C. 2 D. 3 E. 4 The Line will have the same slope irrespective of which two points are taken into account i.e. Slope of Line using Points (4, 2), (3, 1) = Slope of Line using Points (4, 2), (2, a) CONCEPT: Slope between two points (a, b) and (c, d) = (db)/(ca)i.e. (12)/(34) = (a2)/(24) i.e. (a2) = 2 i.e. a = 0 Answer: option A
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If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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30 Jul 2015, 13:25
Bunuel wrote: If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
Little to add here. To solve, either plot out on a graph or calculate the equation of the line, and in turn, solve for \(a\). \(y=mx+b\) \(m = \frac{(21)}{(43)} = 1\) \(y = x + b\) \(2 = 4 + b\) \(b = 2\) if \(y = x  2\), then \(a = 2  2\), and therefore \(a = 0\) IMO A. Since the equation is the first degree, the line is linear, and thus it cannot have the same y value as the other points. So, B or C are out as possible answers automatically. Plotting the others shows that C and D are wrong since the equation is not a quadratic. A. 0B. 1 Out C. 2 Out D. 3 Out E. 4 Out



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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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30 Jul 2015, 13:59
Hi All, Since the 3 points have consecutive Xcoordinate values, we can use 'brute force' to get to the solution without having to do too much math. The points are... (4,2) (3,1) (2,A) Looking at the first two coordinates, the Xcoordinate 'drops' by 1 and the Ycoordinate 'drops' by 1. Since we're told that all 3 points lie on the same line, that 'pattern' will continue. Thus, going from the second coordinate to the third coordinate, since the Xcoordinate 'drops' by 1, the Ycoordinate MUST 'drop' by 1.... 11 = 0 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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30 Jul 2015, 14:20
Bunuel wrote: If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
A. 0 B. 1 C. 2 D. 3 E. 4 IMO: A If the points collinear, then their slopes must be equal. Slope between two points (x1,y1) (x2,y2) is given by =\(\frac{y2y1}{x2x1}\)Thus Slope AB = Slope BC \(\frac{12}{34}\) = \(\frac{a1}{23}\) a= 0
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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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31 Jul 2015, 00:58
slope of line = (43)/(21) = 1 y = mx + c Putting (3,1) in it we get equation of line to be: y = x2 thus, when x = 2, y = a = 0.
Ans.= A



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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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31 Jul 2015, 23:37
If I simply plot all the points in the xy plane, then it can be noticed that when xcoordinate is 2, then y coordinate must be 0 or negative. As answer choices don't include any negative ycoordinate, the answer must be 0.
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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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14 Jul 2016, 08:37
Bunuel wrote: If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
A. 0 B. 1 C. 2 D. 3 E. 4 The first two points tells us that the slope = 21/13 = 1 Meaning all the point has have a constant distance between them Plotting this info in a table we get X Y 4 2 3 1 2 0Answer is A
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Re: If the three points A, B and C with the coordinates (4, 2), (3, 1) and
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28 Nov 2018, 14:37
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