Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49384

In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
Updated on: 13 Nov 2017, 21:24
Question Stats:
60% (01:31) correct 40% (01:31) wrong based on 650 sessions
HideShow timer Statistics
Originally posted by Bunuel on 23 Jul 2015, 10:47.
Last edited by Bunuel on 13 Nov 2017, 21:24, edited 4 times in total.
Edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 49384

In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
26 Oct 2015, 10:02




Current Student
Joined: 20 Mar 2014
Posts: 2638
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
23 Jul 2015, 11:30
mcelroytutoring wrote: DS 136 from OFG 2016 (new question)
y = ax  5 y = x + 6 y = 3x + b
In the xyplane, the straightline graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
1) a = 2
2) r = 17 Solution provided by : mcelroytutoringLet's start by substituting the point (p,r) into all equations in place of (x,y) which will make step #2 a bit easier to comprehend but is not necessary to solve the question. Then, let's consider the number of variables left in each equation. #1: r = ap  5 (3 variables R,A,P) #2: r = p + 6 (2 variables R,P) #3: r = 3p + b (3 variables R,B,P) 1) a = 2 allows us to reduce equation #1 to the variables r and p, which are the same two variables as equation #2. Thus we have simultaneous equations. As soon as we verify that the equations are different, we know that we can solve for both variables. Once we know r and p, we can substitute in equation #3 to solve for b. Sufficient. 2) r = 17 allows us to do the same thing, more or less. It reduces equation #2 to only one variable, allowing us to solve for p. Once we have p (and r), we can use equation #3 to solve for b. Sufficient.
Attachments
Screen Shot 20150723 at 10.36.05 AM.png [ 189.38 KiB  Viewed 12518 times ]
Screen Shot 20150723 at 10.31.01 AM.png [ 30.94 KiB  Viewed 12495 times ]




Director
Joined: 10 Mar 2013
Posts: 546
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
24 Sep 2015, 01:53
if each of the 3 equations contains points (p,r) this means that they intersect in that point 1. a=2 Find the intercept Intercept for three simultaneous equations y=2x5 y=x+6 y=3x+b Let's use the first 2 equations: plug y=x+6 in the secod equation x+6=2x5 > x=11, y=17 we can use the values to calulate b in the 3rd equation 17=33+b > b=16 SUFFICIENT 2. Here we have directly the value for Y, let's plug it in the 2nd equation y=x+6 > 17=x+6 > x=11, y=17; We can plug these values in the 3rd equation and find b as we did above 17=33+b > b=16 SUFFICIENT Answer (D) Most important point is here to catch the hint about intersection of 3 lines at one point
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Intern
Status: GMAT1:520 Q44 V18
Joined: 03 Sep 2015
Posts: 11
Location: United States
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
26 Oct 2015, 10:50
I think it's D.
Keeping point (p,r) in all the equations we get :
p = ar 5 (1) p = r + 6 (2) p = 3r + b (3)
Now consider (1) if a = 2 from (1) and (2) we get r = 11 , p=17 and putting in (3) we can get b.
Similarly for (2) we can get the values for r and p and hence can get the value for b.
So both statements individually are correct to answer the question.



Manager
Joined: 13 Apr 2015
Posts: 75
Concentration: General Management, Strategy
GPA: 3.25
WE: Project Management (Energy and Utilities)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
26 Oct 2015, 19:14
m2k wrote: I think it's D.
Keeping point (p,r) in all the equations we get :
p = ar 5 (1) p = r + 6 (2) p = 3r + b (3)
Now consider (1) if a = 2 from (1) and (2) we get r = 11 , p=17 and putting in (3) we can get b.
Similarly for (2) we can get the values for r and p and hence can get the value for b.
So both statements individually are correct to answer the question. Approach if right but the values you derived are wrong. According to me r = 17 and that is what stmt b also states.



Manager
Joined: 21 Sep 2015
Posts: 79
Location: India
GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
10 Jun 2016, 11:23
y = ax  5 ... eq 1 y = x + 6 ... eq 2 y = 3x + b ...eq 3Total of 4 variables are present.Statement 1 : a = 2Insert in eq 1 We have y = 2x 5 and y = x+6 Solving we get x = 11 and y = 17 Substitute in eq 3 and we get value of b Statement 2: r=17This means the y co ordinate is 17 Substitute in eq 2 we get x as 11 Again can find value of b from equation 3 Hence D
_________________
Appreciate any KUDOS given !



Manager
Joined: 20 Jun 2013
Posts: 55
Location: India
Concentration: Economics, Finance
GPA: 3.5
WE: Information Technology (Other)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
18 Jan 2017, 15:18
we used information from both 1 and 2 then how can the answer be D... should it not be C... some one kindly clarify.......... clearly am a zero in ds and that too a big one



Director
Joined: 14 Nov 2014
Posts: 650
Location: India
GPA: 3.76

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
18 Jan 2017, 20:18
y = ax  51 y = x + 62 y = 3x + b3 In the xyplane, the straightline graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
(1) a = 2 (2) r = 17
All three line intersect each other at common point (p,r). 1. given a = 2 putting in equation 1 .= y=2x5 equating 1(after replacing value of a) and 2 we will get value of (p,r) putting (p,r) in equation 3 we will get value for bsuff..
2 given r = 17. putting in equation 2 we will get value of x.i'e p. Now as we know common point of intersection ,putting p,r in equation 3 , we will get value of b



Manager
Joined: 20 Jun 2013
Posts: 55
Location: India
Concentration: Economics, Finance
GPA: 3.5
WE: Information Technology (Other)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
22 Jan 2017, 15:51
thanks sobby for your response... highly appreciated...



Manager
Joined: 17 Feb 2014
Posts: 102
Location: United States (CA)
GMAT 1: 700 Q49 V35 GMAT 2: 740 Q48 V42
WE: Programming (Computer Software)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
16 Mar 2017, 08:58
(eq1) \(y = ax  5\) (eq2) \(y = x + 6\) (eq3) \(y = 3x + b\)
In the xyplane, the straightline graphs of the three equations above each contain the point (p, r). If a and b are constants, what is the value of b?
1) \(a = 2\) 2) \(r = 17\)
Solution:
1) \(a = 2\)  Putting the value of a in eq1, we get: \(y = 2x  5\)  At this point you can solve for (x, y), plug (x, y) in (eq3) and solve for (b) [though this approach might take few seconds] (alternatively, faster method)  you can skip solving for (x, y) and deduce that given 3 equations and 3 unknowns (since a is given in statement 1) we can solve for all of them (including b), since the lines are have different slopes i.e. different lines. Hence, we can get single value of 'b', proving the condition SUFFICIENT. NOTE: 3 equations and 3 unknowns does not ALWAYS mean that we can find 3 unknown. We have to make sure that 2 of them or all of them are not the same line.
2) \(r = 17\)  Since, point (p, r) lie on all the line, we can plugin the point in above equation \(r = ap  5 => 17 = ap  5\) \(r = p + 6 => 17 = p + 6\) \(r = 3p + b => 17 = 3p + b\)  Again, we do not need to solve for all the variables and just recognize that the above equations will lead to single value of b. Hence, SUFFICIENT.
Answer: (D)



Intern
Joined: 25 Feb 2017
Posts: 37
Location: Korea, Republic of
GPA: 3.67

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
30 Apr 2017, 23:51
y = ax  5 y = x + 6 y = 3x + b
In the xyplane, the straightline graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
1) a = 2
2) r = 17
My 2 cents.
It is important to realize from the Question stem that the 3 equations intersect as (p,r).
For 1), as we know a =2, we can equate the first and second equation to get the value of x, and then use that value of x to find value of y and the find value of b.
For 2), similarly, use r = 17 (which is value of y) to find value of x using the second equation. And then plug it back to the third equation.
So D.



Intern
Joined: 27 Apr 2015
Posts: 8

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
10 Sep 2017, 19:04
Would it be correct to simply say that we have 4 variables with 3 equations so eliminating any one variable gets us to three equations and three variables and is therefore sufficient? Is that logic sound?



Intern
Joined: 11 Sep 2017
Posts: 14

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
13 Nov 2017, 20:21
what is the significance of the the line "In the xyplane, the straightline graphs of the three equations above each contain the point (p,r)",
i solved the problem, but wud have did the same even if they didnt provide line above . as question has 3 equations with 4 variables



BSchool Forum Moderator
Joined: 17 Jun 2016
Posts: 515
Location: India
GMAT 1: 720 Q49 V39 GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
13 Nov 2017, 22:31
Cheryn wrote: what is the significance of the the line "In the xyplane, the straightline graphs of the three equations above each contain the point (p,r)",
i solved the problem, but wud have did the same even if they didnt provide line above . as question has 3 equations with 4 variables The highlighted statement in effect says that all these 3 lines meet each other at one point and so there is a single value of (x,y) that satisfies these 3 equations. It is only because of this highlighted statement you can solve this set of equations for a unique value of x,y, a and b. Hope this clarifies your doubt.
_________________
Compilation of Blogs by Mike Mcgarry  Magoosh



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12443
Location: United States (CA)

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
11 Dec 2017, 14:28
Hi All, We're given the equations for 3 lines (and those equations are based on 4 unknowns: 2 variables and the 2 'constants' A and B): Y = (A)(X)  5 Y = X + 6 Y = 3X + B We're told that the three lines all cross at one point on a graph (p,r). We're asked for the value of B. While this question looks complex, it's actually built around a 'system' math "shortcut"  meaning that since we have 3 unique equations and 4 unknowns, we just need one more unique equation (with one or more of those unknowns) and we can solve for ALL of the unknowns: 1) A =2 With this information, we now have a 4th equation, so we CAN solve for B. Fact 1 is SUFFICIENT 2) R = 17 This information tell us the x coordinate where all three lines will meet, so it's the equivalent of having X=17 to work with. This 4th equation also allows us to solve for B. Fact 2 is SUFFICIENT 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
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835

Re: In the xyplane, the straightline graphs of the three equations above
[#permalink]
Show Tags
02 Jan 2018, 11:00
Bunuel wrote: y = ax  5 y = x + 6 y = 3x + b In the xyplane, the straightline graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
(1) a = 2 (2) r = 17 We can begin by substituting p and r for x and y, respectively, in the three given equations. 1) r = ap – 5 2) r = p + 6 3) r = 3p + b Statement One Alone: a = 2 We can substitute 2 for a in the equation r = ap – 5. Thus, we have: r = 2p – 5 Next we can set equations 1 and 2 equal to each other. 2p – 5 = p + 6 p = 11 Since p = 11, we see that r = 11 + 6 = 17 Finally, we can substitute 11 for p and 17 for r in equation 3. This gives us: 17 = 3(11) + b 17 = 33 + b 16 = b Statement one alone is sufficient to answer the question. Statement Two Alone: r = 17 We can substitute r into all three equations and we have: 1) 17 = ap – 5 2) 17 = p + 6 3) 17 = 3p + b We see that p = 11. Now we can substitute 11 for p in equation 3 to determine a value for b. 17 = 3(11) + b 16 = b Statement two alone is also sufficient to answer the question. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: In the xyplane, the straightline graphs of the three equations above &nbs
[#permalink]
02 Jan 2018, 11:00






