Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Feb 2015
Posts: 3

The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
18 Feb 2015, 02:29
Question Stats:
58% (02:55) correct 42% (03:27) wrong based on 166 sessions
HideShow timer Statistics
The line k has a positive slope m and it passes through the point (4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m? A. 1/4 B. 3/4 C. 5/4 D. 7/4 E. cannot be determined
Official Answer and Stats are available only to registered users. Register/ Login.




Director
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 613
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
18 Feb 2015, 07:02
(Figure attached) Equation of line will be given by y6 / (x (4)) = m or, y = mx + 4m + 6 Area of triangle formed by line k and x and yaxis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given) Simplifying we will get 16m^2 + 48m + 36 = 108m => 16m^2  60m + 36 = 0 => 4m^2  15m + 9 = 0 => 4m^2  12m  3m + 9 =0 => 4m ( m3) 3 (m3) = 0 => m = 3 , 3/4 So, answer will be B Hope it helps! Prjwl99 wrote: The line k has a positive slope m and it passes through the point( 4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m? a)1/4 b)3/4 c)5/4 d)7/4 e)cannot be determined
the ans is B
Could anyone please explain the method for reaching the answer thanks in advance
Attachments
File comment: Figure
figure.png [ 35.81 KiB  Viewed 2830 times ]
_________________
Ankit
Check my Tutoring Site > Brush My Quant
GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief
How to Solve : Statistics  Reflection of a line  Remainder Problems  Inequalities




Manager
Joined: 24 Jan 2015
Posts: 71
GPA: 4
WE: Consulting (Pharmaceuticals and Biotech)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
18 Feb 2015, 08:28
I am not sure if my way of approach is correct. But still I ended up with the answer..
Area of the triangle formed by the line k with X & Y axis is 54. 1/2 * Base * Height = 54
Here Base refers to the xintercept in units and Height refers to the yintercept in units So > X (or Base) * Y (or Height) = 108
We know that the line k passes through the point (4,6) and has a positive slope. Therefore, the point where the line meets the Xaxis must be definitely greater than 4 i.e greater than 4 units from the origin(Base) Similarly, the point where the line meets the Yaxis must be definitely greater than 6 i.e greater than 6 units from the origin(height)
There are a handful of factors that multiply into 108 but only one satisfies the above condition. 9 and 12  valid since it satisfies both of the above criteria
the below ones do not 27 and 4 18 and 6 36 and 3 108 and 1
So the y intercept can be either (0,12) or (0,9) and xintercept can be either (9,0) or (12,0)
We slope m = (y2y1)/(x2x1) > 12/9 or 9/12 i.e 4/3 or 3/4
Answer is 3/4 (B)



SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
18 Feb 2015, 08:39
AVRonaldo wrote: I am not sure if my way of approach is correct. But still I ended up with the answer..
Area of the triangle formed by the line k with X & Y axis is 54. 1/2 * Base * Height = 54
Here Base refers to the xintercept in units and Height refers to the yintercept in units So > X (or Base) * Y (or Height) = 108
We know that the line k passes through the point (4,6) and has a positive slope. Therefore, the point where the line meets the Xaxis must be definitely greater than 4 i.e greater than 4 units from the origin(Base) Similarly, the point where the line meets the Yaxis must be definitely greater than 6 i.e greater than 6 units from the origin(height)
There are a handful of factors that multiply into 108 but only one satisfies the above condition. 9 and 12  valid since it satisfies both of the above criteria
the below ones do not 27 and 4 18 and 6 36 and 3 108 and 1
So the y intercept can be either (0,12) or (0,9) and xintercept can be either (9,0) or (12,0)
We slope m = (y2y1)/(x2x1) > 12/9 or 9/12 i.e 4/3 or 3/4
Answer is 3/4 (B) Your reasoning is ABSOLUTELY SOUND. Now what surprises me is how can someone which such reasoning skills end up with a score of 39 in Quant.
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 07 Aug 2011
Posts: 561
Concentration: International Business, Technology

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
28 Feb 2015, 10:10
Prjwl99 wrote: The line k has a positive slope m and it passes through the point( 4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m? a)1/4 b)3/4 c)5/4 d)7/4 e)cannot be determined
the ans is B
Could anyone please explain the method for reaching the answer thanks in advance check out the attached solution . let me know if case of questions. thanks Lucky Consider +1 Kudos if you like this post.
Attachments
gmatclub.jpg [ 82.22 KiB  Viewed 2677 times ]
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Manager
Joined: 20 Apr 2014
Posts: 101

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
29 Apr 2016, 14:13
Hi Bunuel
Please recognize the approach here. Is it right to try the different factors that produce 108 or you have more reliable and shorter way. Actually, I solved in such way but it took me 4 Mins to complete the operation.



Manager
Joined: 05 Oct 2016
Posts: 93
Location: United States (OH)
GPA: 3.58

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
05 Sep 2017, 10:59
someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers.
_________________
Kudos APPRECIATED!



VP
Joined: 07 Dec 2014
Posts: 1034

The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
Updated on: 06 Sep 2017, 13:12
The line k has a positive slope m and it passes through the point (4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
A. 1/4 B. 3/4 C. 5/4 D. 7/4 E. cannot be determined
assume the line rising from the x axis to (4,6) is the height of a 6810 right triangle thus, the triangle base on the x axis will run 8 units from (4,0) to (12,0) we now know two points on line k: (4,6) and (12,0) m=[60/4(12)]=6/8=3/4 B
Originally posted by gracie on 05 Sep 2017, 16:49.
Last edited by gracie on 06 Sep 2017, 13:12, edited 1 time in total.



Intern
Joined: 31 Aug 2017
Posts: 7

The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
05 Sep 2017, 20:15
SandhyAvinash wrote: someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers. The triangle area is (x*y)/2=54 => x*y=108 Now rise/run=slope => (y6)/(x+4)=m => y=xm+4m+6 => (4m+6)*(4m+6)/m=108 Solve this we find m = 3 or 3/4 Thus answer is B



Manager
Joined: 05 Oct 2016
Posts: 93
Location: United States (OH)
GPA: 3.58

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
06 Sep 2017, 10:51
kelindoan wrote: SandhyAvinash wrote: someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers. The triangle area is (x*y)/2=54 => x*y=108 Now rise/run=slope => (y6)/(x+4)=m => y=xm+4m+6 => (4m+6)*(4m+6)/m=108 Solve this we find m = 3 or 3/4 Thus answer is B hi kelindoan step 3 is still unclear how did you find this statement to solve for m??? please help
_________________
Kudos APPRECIATED!



Manager
Joined: 26 Mar 2016
Posts: 60
Location: India
Concentration: Strategy, General Management
GPA: 3.3
WE: Other (Consulting)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
21 Sep 2017, 00:17
SandhyAvinash wrote: kelindoan wrote: SandhyAvinash wrote: someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers. The triangle area is (x*y)/2=54 => x*y=108 Now rise/run=slope => (y6)/(x+4)=m => y=xm+4m+6 => (4m+6)*(4m+6)/m=108 Solve this we find m = 3 or 3/4 Thus answer is B hi kelindoan step 3 is still unclear how did you find this statement to solve for m??? please help Hi, Hope you understood till equation y=xm+4m+6 Now we need values of x and y intercepts here (nothing but value of x and y) x intercept => 0= xm+4m+6 (place y=0) from her we get x = (4m+6) / m similarly for y intercept , place x = 0 .... so y =4m+6 But the distances x and y are absolute values.. so we can remove negative sign Hope you understood now.. Please let know in case of any doubts.. If it helps, kudos please
_________________
23 Kudos left to unlock next level. Help me by Contributing one for cause .. Please
My failed GMAT experience ... https://gmatclub.com/forum/gmatbadexperience640needsuggestionsonverbalimprovement251308.html
My review on EmpowerGMAT : https://gmatclub.com/reviews/comments/empowergmatonlinecourse345355767



Manager
Joined: 24 Dec 2016
Posts: 79
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
27 May 2018, 22:11
BrushMyQuant wrote: (Figure attached) Equation of line will be given by y6 / (x (4)) = m or, y = mx + 4m + 6 Area of triangle formed by line k and x and yaxis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given) Simplifying we will get 16m^2 + 48m + 36 = 108m => 16m^2  60m + 36 = 0 => 4m^2  15m + 9 = 0 => 4m^2  12m  3m + 9 =0 => 4m ( m3) 3 (m3) = 0 => m = 3 , 3/4 So, answer will be B Hope it helps! Prjwl99 wrote: The line k has a positive slope m and it passes through the point( 4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m? a)1/4 b)3/4 c)5/4 d)7/4 e)cannot be determined
the ans is B
Could anyone please explain the method for reaching the answer thanks in advance Hi Bunuel, BrushMyQuant, Using the 2 points at the X and Y axes and the point through which the line passes, following are the equations for slope that I came up with: \(\frac{(y6)}{(0+4)} = \frac{(60)}{(4x)}\) from this, the equation I get is \(6x4y+xy = 0\) => \(4y=6x 108\) that gives us a slope of 3/2 which isnt an answe choice. Could you please help understand where am I going wrong?



Director
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 613
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: The line k has a positive slope m and it passes through the point (4, [#permalink]
Show Tags
27 May 2018, 22:37
Hi Shruti0805, Couple of things: 1. You are assuming that if a line is passing through point (4,6) then it will pass through (0,6) and (4,0) which is not true. See attached figure for reference. 2. The equation of a line passing through two points is (yy1)/(xx1) = y2y1)/(x2x1) so it will be (y6)/(x0) = (06)/(40) and not (y6)/(0+4) = (60)/(4x) 3. Equation of a line will always be a one degree equation in terms of x and y like ax + by+ c = 0, where a,b,c are constants. hope it helps! Shruti0805 wrote: BrushMyQuant wrote: (Figure attached) Equation of line will be given by y6 / (x (4)) = m or, y = mx + 4m + 6 Area of triangle formed by line k and x and yaxis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given) Simplifying we will get 16m^2 + 48m + 36 = 108m => 16m^2  60m + 36 = 0 => 4m^2  15m + 9 = 0 => 4m^2  12m  3m + 9 =0 => 4m ( m3) 3 (m3) = 0 => m = 3 , 3/4 So, answer will be B Hope it helps! Prjwl99 wrote: The line k has a positive slope m and it passes through the point( 4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m? a)1/4 b)3/4 c)5/4 d)7/4 e)cannot be determined
the ans is B
Could anyone please explain the method for reaching the answer thanks in advance Hi Bunuel, BrushMyQuant, Using the 2 points at the X and Y axes and the point through which the line passes, following are the equations for slope that I came up with: \(\frac{(y6)}{(0+4)} = \frac{(60)}{(4x)}\) from this, the equation I get is \(6x4y+xy = 0\) => \(4y=6x 108\) that gives us a slope of 3/2 which isnt an answe choice. Could you please help understand where am I going wrong?
Attachments
Image.jpg [ 41.91 KiB  Viewed 291 times ]
_________________
Ankit
Check my Tutoring Site > Brush My Quant
GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief
How to Solve : Statistics  Reflection of a line  Remainder Problems  Inequalities




Re: The line k has a positive slope m and it passes through the point (4,
[#permalink]
27 May 2018, 22:37






