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09 Jan 2020, 00:42
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:44) correct
39%
(02:44)
wrong
based on 118
sessions
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Not Attempted Yet
[GMAT math practice question]
A quadrilateral \(P\) has \((1, 1), (3, 1), (3, 5)\) and \((1, 5)\) as \(4\) vertices and another quadrilateral \(Q\) has \((-1, -1), (-5, -1), (-5, -5)\) and \((-1, -5)\) as \(4\) vertices. A line divides these two quadrilaterals evenly at the same time. What is this line?
A. \(y = \frac{- 1}{6}x + \frac{5}{6 }\)
B. \(y = \frac{- 5}{6}x + \frac{1}{6}\)
C. \(y = \frac{ 6}{5}x + \frac{3}{5}\)
D. \(y = \frac{1}{3}x + \frac{5}{6} \)
E. \(y = \frac{- 1}{6}x + \frac{7}{5}\)
A quadrilateral \(P\) has \((1, 1), (3, 1), (3, 5)\) and \((1, 5)\) as \(4\) vertices and another quadrilateral \(Q\) has \((-1, -1), (-5, -1), (-5, -5)\) and \((-1, -5)\) as \(4\) vertices. A line divides these two quadrilaterals evenly at the same time. What is this line?
A. \(y = \frac{- 1}{6}x + \frac{5}{6 }\)
B. \(y = \frac{- 5}{6}x + \frac{1}{6}\)
C. \(y = \frac{ 6}{5}x + \frac{3}{5}\)
D. \(y = \frac{1}{3}x + \frac{5}{6} \)
E. \(y = \frac{- 1}{6}x + \frac{7}{5}\)
09 Jan 2020, 04:43
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MathRevolution
Each quadrilateral is a rectangle.
To divide a rectangle in half, a line must pass through the CENTER of the rectangle.
Center of P = (midpoint of the x-values, midpoint of the y-values) \(= (\frac{1+3}{2}, \frac{1+5}{2}) = (2, 3)\)
Center of Q = (midpoint of the x-values, midpoint of the y-values) \(= (\frac{-1+(-5)}{2}, \frac{-1+(-5)}{2}) = (-3, -3)\)
The correct answer must pass through the two centers (2, 3) and (-3, -3).
Slope of the line that passes through (2, 3) and (-3, -3) \(= \frac{∆y}{∆x} = \frac{-3-3}{-3-2} = \frac{6}{5}\)
General Discussion
09 Jan 2020, 03:33
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By visualizing the two quadrilaterals, we find that one is in the first quadrant, and the other is in the fourth,
so for a line that can pass through them, the slope must be positive ---> this eliminates A,B,E
By trying D, the starting point of the line will be (3 , 1.833) which can't be possibly dividing the quadrilateral in the first quadrant.
By trying C, the starting point of the line will be (3 , 4.166) which can possibly do the trick
C
so for a line that can pass through them, the slope must be positive ---> this eliminates A,B,E
By trying D, the starting point of the line will be (3 , 1.833) which can't be possibly dividing the quadrilateral in the first quadrant.
By trying C, the starting point of the line will be (3 , 4.166) which can possibly do the trick
C
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