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in the coordinate plane, points (x, 1) and (10, y) are

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by varun289 » Fri Dec 14, 2012 8:19 pm
240. In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


my ans - is 11 , but what should real ans ?
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by GMATGuruNY » Fri Dec 14, 2012 9:37 pm
varun289 wrote:240. In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12


my ans - is 11 , but what should real ans ?
The slope of line k is 1/2.
Since the line passes through the origin, the y-intercept is 0.
Thus, the equation of line k is:
y = (1/2)x.

Implication:
For every point on the line, the y-value is 1/2 the x-value.

Thus:
In (x,1), since 1 must be 1/2 the x-value, x=2.
In (10,y), since the y-value must be 1/2 of 10, y=5.

Thus:
x+y = 2+5 =7.

The correct answer is B.
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by puneetkhurana2000 » Fri Dec 14, 2012 11:16 pm
The y intercept is 0 and the equation is y = 1/2 * x

As points (x,1) and (10,y) lie on the line,

So, 1 = x/2 ... x = 2

And y =10/2 ... y = 5

x + y = 2 + 5 = 7

Answer B.
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by varun289 » Sat Dec 15, 2012 3:15 am
my doubt -

y2-y1 / x2-x1 - slope

y-1 / 10-x = 1/2

2y+x=12

now put x=10 , we have y=1 or vice verse put y=1 we get x=10 , so X + Y must be 11 , option C ??

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by GMATGuruNY » Sat Dec 15, 2012 5:06 am
varun289 wrote:my doubt -

y2-y1 / x2-x1 - slope

y-1 / 10-x = 1/2

2y+x=12

now put x=10 , we have y=1 or vice verse put y=1 we get x=10 , so X + Y must be 11 , option C ??

confuses
In y = mx + b, x and y represent the x-coordinate and y-coordinate of any point on the line.
The equation is valid only for combinations of x and y that belong to the SAME POINT.
In (x,1) and (10,y), x and y belong to DIFFERENT points, so they cannot be combined to yield the equation of the line that will have a slope of 1/2 and contain (x,1) and (10,y).
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by Scott@TargetTestPrep » Tue Feb 20, 2018 4:18 pm
varun289 wrote:240. In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12
Since the slope m of the line is ½ and the line passes through (x, 1) and the origin (0,0), we use the slope formula m = (y1 - y2)/(x1 - x2) and we have:


(1 - 0)/(x - 0) = 1/2

1/x = 1/2

x = 2

Similarly, using the points (10, y) and the origin, we can create the equation:

(y - 0)/(10 - 0) = 1/2

y/10 = 1/2

y = 5

Thus, x + y = 2 + 5 = 7.

Answer: B

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