line k has a positive slope m and passes through the point

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Wed Aug 20, 2014 12:08 am
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

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Feb 18, 2015 8:18 am
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
Since the area of the triangle is 54, we get:
(1/2)bh = 54.
bh = 108.

Always look for SPECIAL TRIANGLES.
Answer choice B implies a RISE OF 3 UNITS for every RUN OF 4 UNITS.
A vertical change of 3 and a horizontal change of 4 suggests a 3-4-5 triangle.
Check whether the triangle could be a multiple of a 3-4-5 triangle:
3-4-5
6-8-10
9-12-15
12-16-20.

In the option in red, bh = 12*9 - 108.
If the triangle has a base of 12 and a height of 9, we get the following figure:
Image
Here, the equation of line k is y = (3/4)x + 9.
Since all three points -- (-12, 0), (-4, 6) and (0, 9) -- are on this line, the figure above is valid.
Thus, a slope of 3/4 is a possible value for m.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

User avatar
Master | Next Rank: 500 Posts
Posts: 269
Joined: Sun Apr 27, 2014 10:33 pm
Thanked: 8 times
Followed by:5 members

by prachi18oct » Thu Feb 19, 2015 11:50 am
HI GMATGuruNY

We are considering only if the answer among one of the options is possible. Is that the only reason that we
are not considering the figure with base as 9 and height as 12 ?

I believe since one of the answer choices given is possible so we should not for other possibilities.
Is that correct?

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Feb 19, 2015 2:30 pm
prachi18oct wrote:HI GMATGuruNY

We are considering only if the answer among one of the options is possible. Is that the only reason that we
are not considering the figure with base as 9 and height as 12 ?
We are trying to determine whether 3/4 is a possible slope for line k.

A height of 9 and base of 12 imply the desired slope.
If h=9 and b=12, we get:
(vertical change)/(horizontal change) = 9/12 = 3/4.

A height of 12 and a base of 9 do NOT imply the desired slope.
If h=12 and b=9, we get:
(vertical change)/(horizontal change) = 12/9 = 4/3.

Thus, to determine whether 3/4 is a possible slope for line k, we are considering only h=9 and b=12.
I believe since one of the answer choices given is possible so we should not for other possibilities.
Is that correct?
The question stem asks:
Which of the following could be the value of m?
Since it is possible that m=3/4, there is no need to evaluate the other answer choices.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3