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01 Dec 2020, 01:15
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E
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Difficulty:
95%
(hard)
Question Stats:
28% (02:52) correct
72%
(02:03)
wrong
based on 92
sessions
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A triangle is formed by connecting three points: (0,0), (3,2), and (4m,-1). The line y = mx is then drawn through the triangle, splitting it into two triangles of equal area. What is the sum of all possible values of m?
A. 3/4
B. 1/4
C. 0
D. -1/4
E. -3/4
Are You Up For the Challenge: 700 Level Questions
A. 3/4
B. 1/4
C. 0
D. -1/4
E. -3/4
Are You Up For the Challenge: 700 Level Questions
FauleKatze
GMAT 2: 720 Q48 V40
Posts: 43
Updated on: 01 Dec 2020, 22:35
Originally posted by FauleKatze on 01 Dec 2020, 08:49.
Last edited by FauleKatze on 01 Dec 2020, 22:35, edited 1 time in total.
Last edited by FauleKatze on 01 Dec 2020, 22:35, edited 1 time in total.
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Line y=mx coincides with the median of the triangle, as the line divides the triangle into 2 equal parts.
Midpoint of the side of the triangle, which contains points (4m, -1) and (3,2) = [(3+4m)/2,1/2]
Putting the midpoint in the equation y=mx;
1/2=3m+4(m^2)
m^2+(3/4)m-(1/2)=0
using quadratic equation: m= [-(3/4) + X]/2 and [-(3/4) - X]/2
Adding the two possible values of m, we get -3/4.
Answer: E
Midpoint of the side of the triangle, which contains points (4m, -1) and (3,2) = [(3+4m)/2,1/2]
Putting the midpoint in the equation y=mx;
1/2=3m+4(m^2)
m^2+(3/4)m-(1/2)=0
using quadratic equation: m= [-(3/4) + X]/2 and [-(3/4) - X]/2
Adding the two possible values of m, we get -3/4.
Answer: E
01 Dec 2020, 16:13
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Bunuel
The large triangle is split into two equal areas, so for the graph below, we must have AC = BC (notice the two smaller triangles share the same height when they use the array AB as their base). Then the expression for point C is the midpoint of A and B, which is \((\frac{4m+3}{2}, \frac{1}{2})\). Finally, this point has to be on the line \(y = mx\), we can plug coordinate C into \(y = mx\) to get:
\(\frac{1}{2} = m*\frac{4m+3}{2}\)
\(1 = 4m^2 + 3m\)
\(4m^2 + 3m - 1 = 0\)
\((4m - 1)(m + 1) = 0\)
\(m = \frac{1}{4}\) or \(m = -1\)
Thus the solutions add up to \(\frac{-3}{4}\).
Ans: E
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