Author 
Message 
TAGS:

Hide Tags

Director
Joined: 10 Feb 2006
Posts: 557

In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Apr 2008, 16:49
Question Stats:
75% (01:37) correct 25% (01:51) wrong based on 653 sessions
HideShow timer Statistics
In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=? A. 9 B. 3 C. 7/3 D. 1 E. 1/3
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT the final frontie!!!.




Director
Joined: 14 Aug 2007
Posts: 504

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Apr 2008, 20:29
alimad wrote: In the xycoordinate system, if (a,b) and (a+3,b+k) are two points on the line defined by the equation x = 3y  7, then k =
9 3 7/3 1 1/3
Please provide explaination. Thanks given : y = 1/3x + 7/3 Slope => k/3 = 1/3 i.e K =1




Manager
Joined: 16 Sep 2007
Posts: 158

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Apr 2008, 17:11
x=3*y7 convert to (this step is not necessary but I do it out of habit) y=(x7)/3
substitute a and b for x and y 1. b=(a7)/3
b+k=((a+3)7)/3 substitute equation 1 for b (a7)/3+k=((a+3)7)/3 (a7)/3+k=(a4)/3 a7+3k=a4 3k=3 k=1
D



Director
Joined: 03 May 2007
Posts: 621
Schools: University of Chicago, Wharton School

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Apr 2008, 20:45
alimad wrote: In the xycoordinate system, if (a, b) and (a+3, b+k) are two points on the line defined by the equation x = 3y  7, then k =
9 3 7/3 1 1/3
Please provide explaination. Thanks x = 3y  7 y = 1/3 (x) + 7/3 [(b+k)  b]/ [(a+3)  a] = 1/3 k/3 = 1/3 k = 1 D.



VP
Joined: 10 Jun 2007
Posts: 1051

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Apr 2008, 21:30
alimad wrote: In the xycoordinate system, if (a,b) and (a+3,b+k) are two points on the line defined by the equation x = 3y  7, then k =
9 3 7/3 1 1/3
Please provide explaination. Thanks slope = (y1y2)/(x1x2) = (b+kb) / (a+3a) = k/3 y = x/3 + 7/3, so slope = 1/3 k/3 = 1/3 k = 1



Senior Manager
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 404
Location: United States (NY)
GPA: 3.82
WE: Account Management (Retail Banking)

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
27 Jun 2012, 15:36
Substitute a & b in place of x & y resp... in the eqn. a3b+7=0(i) Substitute a+3 & b+k in the place of x & y resp...we'll get a+3=3(b+k)7 or, a3b3k+10=0(ii) points on the same line will satisfy the equation so , equating (i)&(ii) a3b3k+10=a3b+7 k=1 Ans D
_________________
" Make more efforts " Press Kudos if you liked my post



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9799
Location: Pune, India

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
27 Jun 2012, 23:10
thevenus wrote: Substitute a & b in place of x & y resp... in the eqn. a3b+7=0(i)
Substitute a+3 & b+k in the place of x & y resp...we'll get a+3=3(b+k)7 or, a3b3k+10=0(ii)
Or note here itself that a  3b + 7 = 0 so 3  3k = 0 giving you k = 1
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 114
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
27 Jun 2012, 23:12
thevenus wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D).
Here's my approach:
We are given two points: (a,b) and (a+3,b+k)
We are given an equation of the line: x = 3y  7
Next step is to convert the equation of the line into slopeintercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMATesque.
So the slope of the line is 1/3
Now we know that the equation of the slope of the line is given by:
slope = (y2  y1)/(x2  x1) > Remember, the slope is just "rise" over "run."
That's why we have:
1/3 = [ (b+k)  b ] / [ (a+3)  a]
The two b's will cancel each other in the numerator and so will the two a's in the denominator
We will get 1/3 = k / 3
so 3 / 3 = k
k = 1
_________________
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.  T. Roosevelt



Current Student
Joined: 29 Mar 2012
Posts: 295
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
27 Jun 2012, 23:39
Hi,
Slope of the line x=3y7 is 1/3 so, we can equate the slope of the line to the slope of the points = \(\frac {y_2y_1}{x_2x_1}\) or \(\frac {(b+k)(b)}{(a+3)a} = \frac 13\) or \(\frac k3 = \frac 13\) or k=1,
Answer (D),
Regards,



Intern
Joined: 08 Jul 2014
Posts: 1

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
16 Feb 2015, 07:57
Maple wrote: x=3*y7 convert to (this step is not necessary but I do it out of habit) y=(x7)/3
substitute a and b for x and y 1. b=(a7)/3
b+k=((a+3)7)/3 substitute equation 1 for b (a7)/3+k=((a+3)7)/3 (a7)/3+k=(a4)/3 a7+3k=a4 3k=3 k=1
D x=3*y7 is not y=(x7)/3instead it is y=(x+7)/3 or y=(1/3)x+(7/3) since we know (a,b) and (a+3,b+k) belong to the same line, they must have the same slope, 1/3. [(b+k)b]/[(a+3)a]=1/3 k/3=1/3 k=1



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
16 Feb 2015, 19:16
Hi All, This question can be solved by TESTing VALUES: We're given the equation of a line (X = 3Y  7) and we're told that two points (A, B) and (A+3, B+K) are on this line. We're asked for the value of K. In graphing questions, it sometimes helps to "visualize" the line better if you write the equation in "slopeintercept" format: X = 3Y  7 3Y = X + 7 Y = X/3 + 7/3 For the first coordinate, let's try to keep things simple... X = 0 Y = 7/3 So... A = 0 B = 7/3 For the second coordinate, we have ADD 3 to X.... X = 3 Y = 10/3 So.... A+3 = 3 B+K = 10/3 We know from the first coordinate that B = 7/3, so K = 3/3 = 1 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Director
Joined: 04 Jun 2016
Posts: 547

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
14 Jul 2016, 05:25
alimad wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 Our equation is x=3y7 Lets quickly make it a point intercept form ==> 3y7=x==>3y=x+7==>\(y=\frac{x}{3}+\frac{7}{3}\) Now we can see the coefficient of x is \(\frac{1}{3}\), which by definition is the slope and we know slope =\(\frac{y2y1}{x2x1}\)==> \(\frac{1}{3}=\frac{b+kb}{a+3a}\)==> 1/3=k/3 therefore k=1 Answer is B
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
30 Oct 2017, 13:56
alimad wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 Recall that an ordered pair represents a pair of x and y coordinates. Substituting the values from the first ordered pair (a,b) into the equation, we can create the following equation: a = 3b  7 Substituting the values from the second ordered pair for x and y into the same equation, we have: a + 3 = 3(b + k)  7 → a + 3 = 3b + 3k  7 If we subtract the first equation from the second, we have: 3 = 3k 1 = k Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 16 Oct 2017
Posts: 37

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
26 Jan 2018, 14:27
EMPOWERgmatRichC wrote: Hi All, This question can be solved by TESTing VALUES: We're given the equation of a line (X = 3Y  7) and we're told that two points (A, B) and (A+3, B+K) are on this line. We're asked for the value of K. In graphing questions, it sometimes helps to "visualize" the line better if you write the equation in "slopeintercept" format: X = 3Y  7 3Y = X + 7 Y = X/3 + 7/3 For the first coordinate, let's try to keep things simple... X = 0 Y = 7/3 So... A = 0 B = 7/3 For the second coordinate, we have ADD 3 to X.... X = 3 Y = 10/3 So.... A+3 = 3 B+K = 10/3 We know from the first coordinate that B = 7/3, so K = 3/3 = 1 Final Answer: GMAT assassins aren't born, they're made, Rich Hi Rich, I know the "7/3" came from rewriting to slopeintercept form, but how did you get from "B = 7/3" to "B+K = 10/3"? I know we added 3 to X, but are we adding 3 to Y too?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15498
Location: United States (CA)

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
26 Jan 2018, 15:03
Hi OCDianaOC, Both coordinates have to 'fit' the equation Y = X/3 + 7/3 The first coordinate is (A, B).... and I TESTed VALUES and used (0, 7/3) to define that coordinate. Remember: A = 0 and B = 7/3 The second coordinate is (A+3, B+K).... notice how that's the SAME A and B from the first coordinate. Thus, we have to add 3 to A (so 3+0 = 3) and plug in X=3 into the equation to get the value of the Y.... When X=3.... Y = X/3 + 7/3 Y = (3/3) + 7/3) Y = 10/3 Since the second coordinate is (A+3, B+K), our prior work makes the coordinate (3, 10/3). From the prior work, we see that B = 7/3... B + K = 10/3 (7/3) + K = 10/3 K = 10/3  7/3 = 3/3 = 1 GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



VP
Joined: 09 Mar 2016
Posts: 1229

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Feb 2018, 13:40
gmatsaga wrote: thevenus wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D).
Here's my approach:
We are given two points: (a,b) and (a+3,b+k)
We are given an equation of the line: x = 3y  7
Next step is to convert the equation of the line into slopeintercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMATesque.
So the slope of the line is 1/3
Now we know that the equation of the slope of the line is given by:
slope = (y2  y1)/(x2  x1) > Remember, the slope is just "rise" over "run."
That's why we have:
1/3 = [ (b+k)  b ] / [ (a+3)  a]
The two b's will cancel each other in the numerator and so will the two a's in the denominator
We will get 1/3 = k / 3
so 3 / 3 = k
k = 1
How did you figure out that slope is 1/3 from here Y = x/3 + 7/3 slope is x/3 but how should i know value of X ?



Senior SC Moderator
Joined: 22 May 2016
Posts: 3681

In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Feb 2018, 21:08
alimad wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 \(x = 3y  7\) Rewrite in slopeintercept form \(y = mx + b\)m = slope, b = yintercept, thus: \(3y = x + 7\) => \(y = \frac{1}{3}x + \frac{7}{3}\) Slope = \(\frac{1}{3}\) Slope is also \(\frac{rise}{run}=\frac{(y_2  y_1)}{(x_2  x_1)}\) We have xand ycoordinates for two points: (a,b) and (a+3,b+k) Set the slope equation equal to the slope value \(\frac{(b+k)b}{(a+3)a}=\frac{1}{3}\) \(\frac{b+kb}{a+3a}=\frac{1}{3}\) \(\frac{k}{3}=\frac{1}{3}\) \(3k = 3\) \(k = 1\) Answer D
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has  Margaret Mead



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9799
Location: Pune, India

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
21 Feb 2018, 21:13
dave13 wrote: gmatsaga wrote: thevenus wrote: In the xycoordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y7, then k=?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 My answer is (D).
Here's my approach:
We are given two points: (a,b) and (a+3,b+k)
We are given an equation of the line: x = 3y  7
Next step is to convert the equation of the line into slopeintercept form. We will have Y = x/3 + 7/3. Don't forget this step because you might fall into the trap and decide that the slope of the line is 3. This makes the question very GMATesque.
So the slope of the line is 1/3
Now we know that the equation of the slope of the line is given by:
slope = (y2  y1)/(x2  x1) > Remember, the slope is just "rise" over "run."
That's why we have:
1/3 = [ (b+k)  b ] / [ (a+3)  a]
The two b's will cancel each other in the numerator and so will the two a's in the denominator
We will get 1/3 = k / 3
so 3 / 3 = k
k = 1
How did you figure out that slope is 1/3 from here Y = x/3 + 7/3 slope is x/3 but how should i know value of X ? The equation of a line is y = mx + c where m is the slope and c is the yintercept. So the equation looks like this y = 2x + 4 (m = 2, c = 4) y = x/3 + 5 (m = 1/3, c = 5) etc For more, check out this post: http://www.veritasprep.com/blog/2010/12 ... hegraphs/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4074
Location: Canada

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
03 Sep 2018, 06:58
alimad wrote: In the xycoordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y  7, then k = ?
A. 9 B. 3 C. 7/3 D. 1 E. 1/3 Key Concept: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of that line. Given equation: x = 3 y  7 One point ON the line is ( a, b) So, we can write: a = 3 b  7 Another point ON the line is ( a + 3, b + k) So, we can write: a + 3 = 3( b + k)  7 Expand: a + 3 = 3b + 3k  7 Subtract 3 from both sides to get: a = 3b + 3k  10 We now two equations: a = 3b + 3k  10 a = 3b  7 Subtract the bottom equation from the top equation to get: 0 = 3k  3 Add 3 to both sides: 3 = 3k Solve: k = 1 Answer: D Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Manager
Joined: 29 Jul 2018
Posts: 103
Concentration: Finance, Statistics

Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
Show Tags
14 Nov 2018, 07:35
another solution since x=3y7 is increasing line ie if x increases then y increasing(x will increase by y's constant y will increase by x's constant) hence D




Re: In the xycoordinate system,if (a,b) and (a+3, b+k) are two
[#permalink]
14 Nov 2018, 07:35



Go to page
1 2
Next
[ 22 posts ]



