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:
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
