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

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Status: 1,750 Q's attempted and counting
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WE: Accounting (Accounting)
In the coordinate plane, points (x, 1) and (10, y)  [#permalink]

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New post 17 Nov 2013, 21:36
1
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A
B
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D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:39) correct 24% (02:31) wrong based on 211 sessions

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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


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Re: In the coordinate plane, points (x, 1) and (10, y)  [#permalink]

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New post 17 Nov 2013, 21:41
3
2
avohden wrote:
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


As both the points are on the same line, and the line passes through the origin with a positive slope,
\(\frac{1-0}{x-0} = \frac{1}{2}\) and \(\frac{y-0}{10-0} = \frac{1}{2}\)

Hence, x=2 and y=5

Thus, x+y = 7

B.

IMO more like 550.
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Senior Manager
Senior Manager
User avatar
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 493
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: In the coordinate plane, points (x, 1) and (10, y)  [#permalink]

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New post 20 Nov 2013, 16:43
1

Official Explanation


Answer: B We're given the slope of a line and one point on the line (the origin: 0,0). From this, we can determine every other point on the line. The most direct way to find x and y involves solving for each individually.

We know that slope (1/2, in this case), is equal to the change in y divided by the change in x. Since we know that the line passes through (0,0) and (x,1), we can solve as follows:

1/2 = (1 – 0)/(x – 0)
1/2 = 1/x
x = 2

Use the same approach to solve for y:

1/2 = (y – 0)/(10 – 0)
1/2 = y/10
y = 5

Thus, x + y = 2 + 5 = 7, choice (B).
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Re: In the coordinate plane, points (x, 1) and (10, y)  [#permalink]

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New post 28 Dec 2013, 08:16
1
mau5 wrote:
avohden wrote:
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


As both the points are on the same line, and the line passes through the origin with a positive slope,
\(\frac{1-0}{x-0} = \frac{1}{2}\) and \(\frac{y-0}{10-0} = \frac{1}{2}\)

Hence, x=2 and y=5

Thus, x+y = 7

B.

IMO more like 550.


One can only check the coordiantes and solve

See, we are given that y = 1/2x

So first coordinate since y =1 then x = 2
Second coordinate since x = 1= then y=5

So add em up 2+5 = 7

B

Hope its clear

Cheers
J :)
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Re: In the coordinate plane, points (x, 1) and (10, y)  [#permalink]

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New post 02 Feb 2019, 20:05
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Re: In the coordinate plane, points (x, 1) and (10, y)   [#permalink] 02 Feb 2019, 20:05
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