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# Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What

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Math Expert
Joined: 02 Sep 2009
Posts: 43866
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]

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15 Mar 2015, 22:06
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75% (01:27) correct 25% (02:04) wrong based on 252 sessions

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Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Location: Pune, India
Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink]

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16 Mar 2015, 21:09
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Bunuel wrote:
Attachment:
ppocg_img3.png
Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q?

A. 3
B. 3 1/7
C. 3 2/7
D. 3 3/7
E. 3 1/2

Kudos for a correct solution.

I am surprised no one has solved this question yet!

Using the slope concept, if x co-ordinate increases by 7 (from (– 5, – 1) to (2, 2)), y co-ordinate increases by 3 (from -1 to 2). So when x co-ordinate increases by further 3 (from 2 to 5), the y co-ordinate will increase by (3/7)*3 = 9/7 = 1 (2/7)
So y co-ordinate will become 2 + 1(2/7) = 3 (2/7)
_________________

Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 28 Feb 2014 Posts: 296 Location: United States Concentration: Strategy, General Management Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 17 Mar 2015, 08:50 1 This post received KUDOS 1 This post was BOOKMARKED Here is my approach: m= 2+1 / 2+5 = 3/7 y = (3/7)x + b 2 = (3/7)2 + b b = 8/7 y = (3/7)5 + (8/7) y = 23/7 = 3 2/7 Answer: C Director Joined: 07 Aug 2011 Posts: 578 Concentration: International Business, Technology GMAT 1: 630 Q49 V27 Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 22 Mar 2015, 08:44 5 This post received KUDOS 2 This post was BOOKMARKED Bunuel wrote: Attachment: ppocg_img3.png Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q? A. 3 B. 3 1/7 C. 3 2/7 D. 3 3/7 E. 3 1/2 Kudos for a correct solution. Oops , i am missing a chance to earn a easy kudo . here we go , Slope of line when calculated with (-5,-1) (2,2) = $$3/7$$ Slope of line when calculated with (2,2) (5,q) = $$\frac{q-2}{5-2}$$ $$\frac{q-2}{3} = \frac{3}{7}$$ $$q= 3 \frac{2}{7}$$ _________________ Thanks, Lucky _______________________________________________________ Kindly press the to appreciate my post !! Senior Manager Joined: 02 Mar 2012 Posts: 356 Schools: Schulich '16 Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 22 Mar 2015, 11:04 C slopes are same for all the points so we can equate the slope3/7 to the one with Q co-ordianare getting 23/7 Math Expert Joined: 02 Sep 2009 Posts: 43866 Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 23 Mar 2015, 04:33 Bunuel wrote: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q? A. 3 B. 3 1/7 C. 3 2/7 D. 3 3/7 E. 3 1/2 Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION: Think about this visually. From (–5, –1) to (2, 2), the line moves right 7 and up 3, so that’s a slope of 3/7. From the point (2, 2) to the point (5, Q), there’s a horizontal distance of 3, an unknown vertical distance — call it h, so that h = Q – 2, or Q = h + 2. The ratio of this vertical and horizontal distance must equal the slope. h/3 = 3/7 --> h = 9/7. That’s h. Now, add 2 to get Q. Q = h + 2 = 3 2/7. Answer = (C) _________________ Intern Joined: 12 Apr 2013 Posts: 37 Concentration: Entrepreneurship, Strategy Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 13 May 2015, 09:10 Let the 3 points be A(-5, -1) B(2, 2) and C(5, Q). Equation of line passing through A and B is : (y-y1) = M(x-x1) y + 1 = 3/7( x + 5) .. here slope(M) is calculated as : y2 - y1/x2 -x1( gives 3/7) Since point C(5, Q) passes through the line, so it should satisfy the above equation. Q + 1 = 3/7 (5 + 5) Q = 30/7 - 1 Q = 23/7 or 3 2/7 Option C _________________ Commitment is about stretching your capabilities. It can take you across all obstacles!! Non-Human User Joined: 09 Sep 2013 Posts: 13800 Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 01 Oct 2016, 00:29 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 24 Dec 2016 Posts: 74 Location: India Concentration: Finance, General Management WE: Information Technology (Computer Software) Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 25 Feb 2017, 05:54 As slope for the line remains constant, slope between (-5,-1) and (2,2) would be the same. thus, {2- (-1)}/{2-(-5)} = (Q-2)/(5-2) => 3/7=(Q-2)/3 => Q-2=9/7 => Q=23/7 = 3 2/7 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7951 Location: Pune, India Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What [#permalink] ### Show Tags 09 Apr 2017, 23:38 VeritasPrepKarishma wrote: Bunuel wrote: Attachment: ppocg_img3.png Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What is the value of Q? A. 3 B. 3 1/7 C. 3 2/7 D. 3 3/7 E. 3 1/2 Kudos for a correct solution. I am surprised no one has solved this question yet! Using the slope concept, if x co-ordinate increases by 7 (from (– 5, – 1) to (2, 2)), y co-ordinate increases by 3 (from -1 to 2). So when x co-ordinate increases by further 3 (from 2 to 5), the y co-ordinate will increase by (3/7)*3 = 9/7 = 1 (2/7) So y co-ordinate will become 2 + 1(2/7) = 3 (2/7) Answer (C) Responding to a pm: Quote: I really did not understand how did u get 2 ahead of 9/7. Also, the concept of slopes that you used, can u explain it to me. I do understand that slopes is rise/ run. or I have read it in school as Tan angle that line makes with x -axis. Now, the approach you used I drew inference that Slope is with an increase in an x coordinate the y coordinate increases with according to slope . If you write $$\frac{9}{7}$$ in mixed fractions, you get $$1\frac{2}{7}$$. As for the slope concept, I have explained it in detail in this blog post: https://www.veritasprep.com/blog/2016/0 ... line-gmat/ Take a look and get back to me if any doubts remain. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Line J passes through the points (– 5, – 1), (2, 2), and (5, Q). What   [#permalink] 09 Apr 2017, 23:38
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