It is currently 20 Feb 2018, 13:42

### 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

# How many integral values of k are possible, if the lines 3x+

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 155
How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

09 Mar 2011, 22:43
2
KUDOS
24
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

33% (03:18) correct 67% (02:46) wrong based on 194 sessions

### HideShow timer Statistics

How many integral values of k are possible, if the lines 3x+4ky+6 = 0, and kx-3y+9 = 0 intersect in the 2nd quadrant.

A. 5
B. 4
C. 3
D. 6
E. 2
[Reveal] Spoiler: OA
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 863
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:15
I got -0.5 < k < 4.5

hence the integral values are 0,1,2,3,4. should be B. Please check. I am not a fan of algebra, sorry

vjsharma25 wrote:
How many integral values of k are possible,if the lines
3x+4ky+6 = 0, and kx-3y+9 = 0 intersect in the 2nd quadrant.

A) 5 B) 4 C) 3 D) 6 E) 2

I was able to do it but I am not convinced by my approach.

Last edited by gmat1220 on 09 Mar 2011, 23:26, edited 1 time in total.
Manager
Joined: 10 Nov 2010
Posts: 155
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:24
gmat1220 wrote:
I got -0.5 < k < 3.375

hence the integral values are 0,1,2,3. should be B

vjsharma25 wrote:
How many integral values of k are possible,if the lines
3x+4ky+6 = 0, and kx-3y+9 = 0 intersect in the 2nd quadrant.

A) 5 B) 4 C) 3 D) 6 E) 2

I was able to do it but I am not convinced by my approach.

Can you explain how you got this range?
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 863
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:32
2
KUDOS
1
This post was
BOOKMARKED
solving for values of x and y from original equations. And knowing x < 0 and y > 0 in II quadrant.
x = -18 - 36k / (4k^2 + 9)
y = (108 - 24k) / 4 (4k^2 + 9)

Hence -18 - 36 k < 0
So k > -0.5

And 108 - 24k >0
k < 108 / 24
k < 18 / 4
k < 9/2
k < 4.5

-0.5 < k < 4.5

Phew !
Manager
Joined: 10 Nov 2010
Posts: 155
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:44
@gmat1220
But now you got the correct range and correct answer .

I was not taking values of x and y as independent. Thats why i got confused.
Thanks for the explanation.
Manager
Joined: 14 Feb 2011
Posts: 181
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:46
4
KUDOS
2
This post was
BOOKMARKED
vjsharma25 wrote:
How many integral values of k are possible,if the lines
3x+4ky+6 = 0, and kx-3y+9 = 0 intersect in the 2nd quadrant.

A) 5 B) 4 C) 3 D) 6 E) 2

I was able to do it but I am not convinced by my approach.

We are given

$$3x+4ky = -6$$ .... (1) and
$$kx-3y = -9$$ ........(2)

Lets calculate their intersection point in terms of k

Multiply (1) by k and (2) by 3 and then subtract (2) from (1) to solve for y, we will get

$$(4k^2+9)*y = 27-6k$$ or $$y = (27-6k)/(4k^2+9)$$.... (3)

Now, multiply (2) by 4/3k and then add (1) and (2) to solve for x, we will get

$$x = -3*(12k+6)/(4k^2+9)$$.... (4)

We know that these intersection points lie in 2nd quadrant, so y has be positive and x has to be negative

y is positive when $$27-6k > 0$$or $$k < 4.5$$
Similarly, x is negative when $$12+6k > 0$$ or $$k > -0.5$$

So, we have -0.5<k<4.5, so it can take integer values of 0,1,2,3,4. Hence, five values.

This is tedious approach and takes at least 2.5 to 3 minutes.

I don't know of a faster way to do so

Last edited by beyondgmatscore on 09 Mar 2011, 23:49, edited 1 time in total.
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 863
Re: How many integral values of k are possible [#permalink]

### Show Tags

09 Mar 2011, 23:48
1
This post was
BOOKMARKED
Man this was monster ! especially my equations go completely haywire when I look at algebra.
Non-Human User
Joined: 09 Sep 2013
Posts: 13815
Re: How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

05 Sep 2014, 14:17
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.
_________________
Current Student
Joined: 29 May 2013
Posts: 115
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

29 Jun 2015, 21:49
Can someone pls explain how to arrive at these 2 equations mentioned above.
x = -18 - 36k / (4k^2 + 9)
y = (108 - 24k) / 4 (4k^2 + 9)
Manager
Joined: 20 Jul 2011
Posts: 81
GMAT 1: 660 Q49 V31
Re: How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

29 Jun 2015, 22:34
1
This post was
BOOKMARKED
jayanthjanardhan wrote:
Can someone pls explain how to arrive at these 2 equations mentioned above.
x = -18 - 36k / (4k^2 + 9)
y = (108 - 24k) / 4 (4k^2 + 9)

The given equations are

3x + 4ky = -6 ------1
kx - 3y = -9 ------2

Try solving the two equations:

1. Multiply eq 1 by k, 3kx + 4k^2y = -6k ---------3
2. Multiply eq 2 by 3, 3kx - 9y = -27 ---------4

Solving eq, 3 and 4, we can get the value of y.

where y = (27-6k)/(4k^2 + 9)..

Since y should be > 0, 27-6k > 0, solving k<4.5

Similarly, solving for x gives or sub y in eq 2 , x = -6(6k+3) / 4k^2 + 9

since x < 0, 6k+3 should be > 0 => 6k+3 > 0, solving k < -0.5

Hence k has 5 Integral values 0, 1, 2, 3 and 4.
Non-Human User
Joined: 09 Sep 2013
Posts: 13815
Re: How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

06 Aug 2016, 02:19
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13815
Re: How many integral values of k are possible, if the lines 3x+ [#permalink]

### Show Tags

26 Aug 2017, 20:51
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.
_________________
Re: How many integral values of k are possible, if the lines 3x+   [#permalink] 26 Aug 2017, 20:51
Display posts from previous: Sort by