If the three points A, B and C with the coordinates (4, 2), (3, 1) and

Question

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

GMATinsight · Answer

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) = (d-b)/(c-a)

i.e. (1-2)/(3-4) = (a-2)/(2-4)

i.e. (a-2) = -2

i.e. a = 0

Answer: option A

mejia401 · Answer

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{(2-1)}{(4-3)} = 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. 0 
 B. 1 Out
C. 2 Out
D. 3 Out
E. 4 Out

EMPOWERgmatRichC · Answer

Hi All,

Since the 3 points have consecutive X-co-ordinate 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 co-ordinates, the X-coordinate 'drops' by 1 and the Y-co-ordinate '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 co-ordinate to the third co-ordinate, since the X-coordinate 'drops' by 1, the Y-co-ordinate MUST 'drop' by 1....

1-1 = 0

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

VenoMfTw · Answer

IMO: A

If the points collinear, then their slopes must be equal.

Slope between two points (x1,y1) (x2,y2) is given by = \frac{y2-y1}{x2-x1}

Thus Slope AB = Slope BC
 \frac{1-2}{3-4}  =  \frac{a-1}{2-3} 
a= 0

AA2014 · Answer

slope of line = (4-3)/(2-1) = 1
y = mx + c
Putting (3,1) in it we get equation of line to be:- y = x-2
thus, when x = 2, y = a = 0.

Ans.= A

zmtalha · Answer

If I simply plot all the points in the xy plane, then it can be noticed that when x-coordinate is 2, then y coordinate must be 0 or negative.
As answer choices don't include any negative y-coordinate, the answer must be 0.

LogicGuru1 · Answer

The first two points tells us that the slope = 2-1/1-3 = 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   0

Answer is A

bumpbot · Answer

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If the three points A, B and C with the coordinates (4, 2), (3, 1) and

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If the three points A, B and C with the coordinates (4, 2), (3, 1) and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards