For what values of k will the pair of equations 3x + 4y = 12 and kx + : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 08:26

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For what values of k will the pair of equations 3x + 4y = 12 and kx +

Author Message
TAGS:

### Hide Tags

Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 116 [2] , given: 1

For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

13 Apr 2007, 00:22
2
KUDOS
17
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:09) correct 31% (02:16) wrong based on 443 sessions

### HideShow timer Statistics

For what values of k will the pair of equations 3x + 4y = 12 and kx + 12y = 30 does not have a unique solution?

A. 12
B. 9
C. 3
D. 7.5
E. 2.5
[Reveal] Spoiler: OA
Director
Joined: 14 Jan 2007
Posts: 777
Followers: 2

Kudos [?]: 134 [5] , given: 0

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

13 Apr 2007, 02:51
5
KUDOS
3
This post was
BOOKMARKED
A system of linear equations with a unique solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.
So we have to find out the the value K so that the lines become parallel. Parallel lines don't intersect each other. That's why having no unique solution.

Two parallel lines have their slopes equal.
Slope of the line 3x+4y = 12, = -3/4

Putting K =9 in the line kx+12y = 30 , slope of this line = -3/4

Hence for k =9 the second line is parallel to the first one. Hence the lines will not have a unique solution.
SVP
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 146 [1] , given: 0

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

13 Apr 2007, 03:00
1
KUDOS
1
This post was
BOOKMARKED
(B) as well... I agree with what vshaunak@gmail.com said above

For 2 equations of line, we have 3 possible cases:
> 1 point intersect the 2 lines = 2 different slopes for the lines
> No intersection = Same slopes and different Y-interceptors
> Infinite number of interesections = Same slopes and same Y-interceptors

So, the question just asks us for which value of k, the slopes are equal.

o 3x+4y = 12
<=> y = -3/4 * x + 12

o kx+12y = 30
<=> y = -k/12 * x + 30/12

By equalizing the 2 slopes, we have:
-k/12 = -3/4
<=> k = 12*3/4 = 9
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5062
Location: Singapore
Followers: 30

Kudos [?]: 348 [0], given: 0

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

13 Apr 2007, 06:08
1
This post was
BOOKMARKED
2x+4y = 12 --> 4y = 12-2x --> y = -0.5x+3
kx+12y = 30 --> 12y = -kx+30 --> y = -kx/12 +2.5

The pairs will not have a unique solution if the lines are parallel. To find this, just make sure both lines have similar slopes. Above, I have place the equations in the standard straight-line equation y = mx+c where m is the gradient of the line and c is the y-intercept.

so since y = -0.5x+3 has a gradient of -0.5, then we must make sure y = kx/12+2.5 has a gradient of -0.5 too. To have this, we need k = 9.
Intern
Joined: 13 Oct 2005
Posts: 10
Followers: 0

Kudos [?]: 2 [0], given: 3

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

09 Jan 2012, 00:47
Hi Guys, let me know if this approach is correct(its a shortcut though):)
solving the two eq simultaneously, we get kx-9x=18
so for any value except 9 for K we ill have a unique solution. so 9 is our answer.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

24 Sep 2015, 10:36
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.
_________________
Intern
Joined: 14 Jan 2016
Posts: 1
Location: India
Concentration: General Management, Finance
GPA: 3.56
Followers: 0

Kudos [?]: 0 [0], given: 7

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

18 Jan 2016, 07:45
A linear equation in two variables may have : 1 solution(intersecting lines), infinite solution(overlapping lines) or no solution (parallel lines)

For a system of equations to not have a unique solution, there should either be no solution or infinite solutions.

ax+by= c
px+qy=r

These will have no solution when :-
(a/p) = (b/q) =/= (c/r)

These will have infinite solutions when :-
(a/p) = (b/q) = (c/r)

As 4/12 =/= 12/30, thus the system should not have any solution.
4/12 = 1/3 thus 3/k = 1/3
k = 3*3 = 9.
_________________

The only alternative to hard work is HARDER work.

Intern
Joined: 09 Aug 2015
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 220

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

15 May 2016, 22:45
i approached this problem in slightly different way,

we have 2 equations
1. 3x + 4y = 12 -- > 9x + 12y = 36

2. kx + 12y = 30

substract 1-2, we get (9-K)x = 6

i.e. x = 6/(9-k)

then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Intern
Joined: 06 May 2016
Posts: 18
WE: Education (Education)
Followers: 0

Kudos [?]: 8 [2] , given: 5

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

16 May 2016, 01:24
2
KUDOS
To solve two variables we need two distinct equations.

If X and Y are in the same ratio in both equations we cannot solve it.

Y1:Y2
4:12
1:3

So if X1:X2 is in the ratio 1:3 there is no distinct equation
1:3
3:9

(B) If X = 9 there is no solution.
Intern
Joined: 06 Dec 2014
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 72

Re: For what values of k will the pair of equations 3x + 4y = 12 and kx + [#permalink]

### Show Tags

19 Oct 2016, 05:59
This can also be approached this way.

Multiply 3x+4y=12 with 3 and replace 12 y with 30-kx.

This gives us x(9-k)-6. Hence, x= 6/(9-k). We get value for x for everything besides k=9 as that makes the denominator 0.

Hope this helps
Re: For what values of k will the pair of equations 3x + 4y = 12 and kx +   [#permalink] 19 Oct 2016, 05:59
Similar topics Replies Last post
Similar
Topics:
1 (3x + 2) (2x - 5) = ax² + kx + n . What is the value of a - n + k ? 2 12 May 2016, 00:45
2 For which value of k does the following pair of equations yield a 1 10 Nov 2015, 20:24
3 If f(x) = k(x - k) and k is a constant, what is the value 3 24 Oct 2013, 09:26
4 If one root of the equation 2x^2 + 3x – k = 0 is 6, what is the value 6 17 Apr 2011, 08:17
In the square above, 12w = 3x = 4y. What fractional part of the square 6 04 Aug 2008, 09:34
Display posts from previous: Sort by