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
line k has a positive slope m and passes through the point
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Since the area of the triangle is 54, we get: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
(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.
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- prachi18oct
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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?
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?
- GMATGuruNY
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We are trying to determine whether 3/4 is a possible slope for line k.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 ?
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.
The question stem asks:I believe since one of the answer choices given is possible so we should not for other possibilities.
Is that correct?
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.
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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.
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