GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 26 May 2019, 16:55

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In the xy-coordinate system,if (a,b) and (a+3, b+k) are two

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Director
Director
avatar
Joined: 10 Feb 2006
Posts: 622
In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Apr 2008, 16:49
3
14
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:38) correct 26% (01:52) wrong based on 720 sessions

HideShow timer Statistics

In the xy-coordinate 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

_________________
GMAT the final frontie!!!.
Manager
Manager
User avatar
Joined: 16 Sep 2007
Posts: 204
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Apr 2008, 17:11
3
1
1
x=3*y-7
convert to (this step is not necessary but I do it out of habit)
y=(x-7)/3

substitute a and b for x and y
1. b=(a-7)/3

b+k=((a+3)-7)/3
substitute equation 1 for b
(a-7)/3+k=((a+3)-7)/3
(a-7)/3+k=(a-4)/3
a-7+3k=a-4
3k=3
k=1

D
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 651
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Apr 2008, 20:29
2
alimad wrote:
In the xy-coordinate 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
Director
Director
User avatar
Joined: 03 May 2007
Posts: 769
Schools: University of Chicago, Wharton School
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Apr 2008, 20:45
1
2
alimad wrote:
In the xy-coordinate 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
VP
avatar
Joined: 10 Jun 2007
Posts: 1324
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Apr 2008, 21:30
1
1
1
alimad wrote:
In the xy-coordinate 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 = (y1-y2)/(x1-x2) = (b+k-b) / (a+3-a) = k/3
y = x/3 + 7/3, so slope = 1/3

k/3 = 1/3
k = 1
Senior Manager
Senior Manager
User avatar
B
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 424
Location: United States (NY)
GPA: 3.82
WE: Account Management (Retail Banking)
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 27 Jun 2012, 15:36
2
Substitute a & b in place of x & y resp... in the eqn.
a-3b+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,
a-3b-3k+10=0-------(ii)

points on the same line will satisfy the equation so ,

equating (i)&(ii)
a-3b-3k+10=a-3b+7
k=1

Ans- D
_________________
" Make more efforts "
Press Kudos if you liked my post
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9246
Location: Pune, India
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 27 Jun 2012, 23:10
thevenus wrote:
Substitute a & b in place of x & y resp... in the eqn.
a-3b+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,
a-3b-3k+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
Manager
User avatar
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 118
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 27 Jun 2012, 23:12
1
thevenus wrote:
In the xy-coordinate 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



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 slope-intercept 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 GMAT-esque. 8-)

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
User avatar
B
Joined: 29 Mar 2012
Posts: 302
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 27 Jun 2012, 23:39
3
Hi,

Slope of the line x=3y-7 is 1/3
so, we can equate the slope of the line to the slope of the points = \(\frac {y_2-y_1}{x_2-x_1}\)
or \(\frac {(b+k)-(b)}{(a+3)-a} = \frac 13\)
or \(\frac k3 = \frac 13\)
or k=1,

Answer (D),

Regards,
Intern
Intern
avatar
Joined: 08 Jul 2014
Posts: 1
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 16 Feb 2015, 07:57
Maple wrote:
x=3*y-7
convert to (this step is not necessary but I do it out of habit)
y=(x-7)/3

substitute a and b for x and y
1. b=(a-7)/3

b+k=((a+3)-7)/3
substitute equation 1 for b
(a-7)/3+k=((a+3)-7)/3
(a-7)/3+k=(a-4)/3
a-7+3k=a-4
3k=3
k=1

D

x=3*y-7 is not y=(x-7)/3
instead 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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14209
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 16 Feb 2015, 19:16
3
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 "slope-intercept" format:

X = 3Y - 7

3Y = X + 7
Y = X/3 + 7/3

For the first co-ordinate, let's try to keep things simple...
X = 0
Y = 7/3

So...
A = 0
B = 7/3

For the second co-ordinate, we have ADD 3 to X....
X = 3
Y = 10/3

So....
A+3 = 3
B+K = 10/3

We know from the first co-ordinate that B = 7/3, so K = 3/3 = 1

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

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Director
Director
User avatar
B
Joined: 04 Jun 2016
Posts: 563
GMAT 1: 750 Q49 V43
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 14 Jul 2016, 05:25
alimad wrote:
In the xy-coordinate 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


Our equation is x=3y-7
Lets quickly make it a point intercept form ==> 3y-7=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 =\(\frac{y2-y1}{x2-x1}\)==> \(\frac{1}{3}=\frac{b+k-b}{a+3-a}\)==> 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 semi-retired.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 30 Oct 2017, 13:56
alimad wrote:
In the xy-coordinate 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


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
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star 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
Intern
avatar
B
Joined: 16 Oct 2017
Posts: 37
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 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 "slope-intercept" format:

X = 3Y - 7

3Y = X + 7
Y = X/3 + 7/3

For the first co-ordinate, let's try to keep things simple...
X = 0
Y = 7/3

So...
A = 0
B = 7/3

For the second co-ordinate, we have ADD 3 to X....
X = 3
Y = 10/3

So....
A+3 = 3
B+K = 10/3

We know from the first co-ordinate 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 slope-intercept 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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14209
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 26 Jan 2018, 15:03
Hi OCDianaOC,

Both co-ordinates have to 'fit' the equation Y = X/3 + 7/3

The first co-ordinate is (A, B).... and I TESTed VALUES and used (0, 7/3) to define that co-ordinate. Remember: A = 0 and B = 7/3

The second co-ordinate is (A+3, B+K).... notice how that's the SAME A and B from the first co-ordinate. 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 co-ordinate is (A+3, B+K), our prior work makes the co-ordinate (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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1283
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Feb 2018, 13:40
gmatsaga wrote:
thevenus wrote:
In the xy-coordinate 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



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 slope-intercept 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 GMAT-esque. 8-)

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
avatar
V
Joined: 22 May 2016
Posts: 2772
In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Feb 2018, 21:08
1
alimad wrote:
In the xy-coordinate 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

\(x = 3y - 7\)

Rewrite in slope-intercept form
\(y = mx + b\)
m = slope, b = y-intercept, 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 x-and y-coordinates for two points:
(a,b) and (a+3,b+k)

Set the slope equation equal to the slope value

\(\frac{(b+k)-b}{(a+3)-a}=\frac{1}{3}\)

\(\frac{b+k-b}{a+3-a}=\frac{1}{3}\)

\(\frac{k}{3}=\frac{1}{3}\)

\(3k = 3\)

\(k = 1\)

Answer D
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9246
Location: Pune, India
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 21 Feb 2018, 21:13
dave13 wrote:
gmatsaga wrote:
thevenus wrote:
In the xy-coordinate 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



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 slope-intercept 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 GMAT-esque. 8-)

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 y-intercept.
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 ... he-graphs/
_________________
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 >
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3729
Location: Canada
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 03 Sep 2018, 06:58
Top Contributor
1
alimad wrote:
In the xy-coordinate 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 = 3y - 7
One point ON the line is (a, b)
So, we can write: a = 3b - 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
Image
Manager
Manager
avatar
B
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics
GMAT 1: 620 Q45 V31
GMAT ToolKit User
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two  [#permalink]

Show Tags

New post 14 Nov 2018, 07:35
another solution since x=3y-7 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
GMAT Club Bot
Re: In the xy-coordinate system,if (a,b) and (a+3, b+k) are two   [#permalink] 14 Nov 2018, 07:35

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

In the xy-coordinate system,if (a,b) and (a+3, b+k) are two

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.