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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # In the coordinate plane, points (x, 1) and (10, y) are on li  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Status: Pushing Hard Affiliations: GNGO2, SSCRB Joined: 30 Sep 2012 Posts: 79 Location: India Concentration: Finance, Entrepreneurship GPA: 3.33 WE: Analyst (Health Care) In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 03 May 2013, 17:43 3 3 00:00 Difficulty: 15% (low) Question Stats: 78% (01:46) correct 22% (02:23) wrong based on 280 sessions ### HideShow timer Statistics 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 _________________ If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 04 May 2013, 03:46 5 3 manishuol 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 Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x. Thus: (x, 1)=(2, 1) and (10, y) = (10, 5) --> x+y=2+5=7. Answer: B. _________________ ##### General Discussion MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 5887 City: Pune Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 04 May 2013, 06:52 4 1 We know the equation of any line is y=mx+c Where m = slope and c = y intercept (point where line crosses y axis) Since line passes thru origin then y intercept (i.e. C) must be zero we also know m = slope = 1/2 so the equation becomes y=$$\frac{x}{2}$$ we are given two points that are on line (x,1) (10,y) Plug second point (10,y) in to the equation y=$$\frac{10}{2}$$ --------> y=5 Plug First point (x,1) in to the equation 1=$$\frac{x}{2}$$ -----------> x=2 x+y = 7 Choice B Regards, Narenn _________________ Intern Joined: 23 Apr 2013 Posts: 21 Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 04 May 2013, 10:02 manishuol 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 Equation of a line passing through origin and having a slope m is given by $$y = mx$$ Hence the equation of the given line is $$y = 0.5 * x$$ This gives the values of x and y as 2 and 5 respectively. Hence x + y = 7 Correct Answer is B Manager Joined: 24 Apr 2013 Posts: 60 Location: United States Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 21 Oct 2013, 10:18 My approach was to apply the rise/run=slope rule so, y-1/10-x = 1/2 2y-2=10-x 2y+x=12, substitute with one of the given points (x,1) 2(1) +x=12, x=10, y=1, x+y=11 can someone please tell me why this approach doesn't work? _________________ Struggling: make or break attempt MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 5887 City: Pune Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 21 Oct 2013, 10:40 SaraLotfy wrote: My approach was to apply the rise/run=slope rule so, y-1/10-x = 1/2 2y-2=10-x 2y+x=12, substitute with one of the given points (x,1) 2(1) +x=12, x=10, y=1, x+y=11 can someone please tell me why this approach doesn't work? IMO what you have obtained (2y+x=12) is the algebraic equation, but it is not the equation of a line. Equation of line is described as y=mx+c ------> where 'm' is the slope of a line and 'c' is the 'y' intercept. Per the equation 2y+x=12 $$m=slope=-\frac{1}{2}$$ (which is not correct. The slope is $$\frac{1}{2}$$) c=y intercept = 6 (This is also not correct. We know that line is passing thru origin, so its y intercept (the y value of point where line crosses 'y' axis) must be zero. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13095 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the coordinate plane, points (x, 1) and (10, y) are on li [#permalink] ### Show Tags 26 May 2015, 20:52 Hi All, This question has a great "brute force" element to it. Since we know that the line passes through the Origin (0,0) and has a slope of 1/2, we can "map out" as many co-ordinates as we need to to answer the given question. Since the slope is 1/2, for every increase of 2 in the X-coordinate we have an increase of 1 in the Y-coordinate: (0,0) (2,1) (4,2) (6,3) (8,4) (10, 5) We're told that (X,1) and (10,Y) are on the line. We're asked for the value of X+Y.... From our list of co-ordinates, we can see that X = 2 and Y = 5... X+Y = 2+5 = 7 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: In the coordinate plane, points (x, 1) and (10, y) are on li  [#permalink]

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27 May 2016, 06:29
Slope m = (y2 - y1) / (x2 - x1) ---formula equation

there are three points on the line (0,0) , (x,1) and (10,y).

given m = 1/2.

first take (0,0) , (x,1) and m=1/2 and put these in formula equation and we get
1/2 = 1-0 / x-0 hence x=2

first take (0,0) , (10,y) and m=1/2 and put these in formula equation and we get
1/2 = y-0 / 10-0 hence y=5

x+y = 5+2 = 7.
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In the coordinate plane, points (x, 1) and (10, y) are on li  [#permalink]

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14 Feb 2018, 11:52
manishuol 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

Hi niks18 please let me know if my solution/ approach is correct ?

$$\frac{1-y}{x-10}=\frac{1}{2}$$ cross multiply

$$2-2y = x-10$$

$$x-10-2+2y$$

$$x+2y-12 = 0$$

$$2y= 12-x$$

$$y = \frac{-x}{2}+ 6$$

now since I know that slop is $$1/2$$ hence x = 1 and y intercept is 6

so x+y = 1+6 = 7

many thanks!
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Re: In the coordinate plane, points (x, 1) and (10, y) are on li  [#permalink]

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15 Feb 2018, 02:14
1
dave13 wrote:
manishuol 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

Hi niks18 please let me know if my solution/ approach is correct ?

$$\frac{1-y}{x-10}=\frac{1}{2}$$ cross multiply

$$2-2y = x-10$$

$$x-10-2+2y$$

$$x+2y-12 = 0$$

$$2y= 12-x$$

$$y = \frac{-x}{2}+ 6$$

now since I know that slop is $$1/2$$ hence x = 1 and y intercept is 6

so x+y = 1+6 = 7

many thanks! :)

Hi dave13,

what you have done is used the formula to find slope and converted it to an algebraic equation which does not represent the equation of line.

equation of line is $$y=mx+c$$, where $$m$$ is slope of the line

as per your equation $$y=\frac{-1}{2}x+6$$, so here slope, $$m=\frac{-1}{2}$$ which is incorrect.

We know that the line passes through the origin so our equation should be

$$y=\frac{1}{2}x+c$$ and at origin we have (0,0)

so $$0=\frac{1}{2}*0+c => c=0$$ i.e y-intercept is 0 (as per your equation y intercept is 6 which is incorrect). If a line passes through origin it will not cut y-axis and hence there will be no intercept.

Hence equation of line will be $$y=\frac{1}{2}x$$

now at (x,1) we will have $$1=\frac{1}{2}x=>x=2$$

and at (10,y) we will have $$y=\frac{1}{2}*10 =>y=5$$

Hence $$x+y=2+5=7$$

There is an alternate method as well using only the formula to find slope. This method is also explained in earlier posts.
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Re: In the coordinate plane, points (x, 1) and (10, y) are on li  [#permalink]

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20 Feb 2018, 16:14
1
manishuol 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

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.

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Re: In the coordinate plane, points (x, 1) and (10, y) are on li &nbs [#permalink] 20 Feb 2018, 16:14
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