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02 Jun 2015, 06:36
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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:
55%
(hard)
Question Stats:
65% (02:27) correct
35%
(02:49)
wrong
based on 670
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the quadrilateral bounded by the lines and \(y = \frac{3}{4}*x + 6\), \(y= \frac{3}{4}*x - 6\), \(y= -\frac{3}{4}*x + 6\), \(y = -\frac{3}{4}*x - 6\) ?
(A) 48
(B) 64
(C) 96
(D) 100
(E) 140
(A) 48
(B) 64
(C) 96
(D) 100
(E) 140
02 Jun 2015, 09:36
Kudos
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When you try to draw it, this becomes very clear.
See attached figure.
y = 3/4 x + 6 has y intercept 6 and x intercept is -8(put y =0 in the equation and calculate for x). So the line passes through (0,6) and (-8,0)
y = 3/4 x - 6 has y intercept -6 and x intercept is 8. So the line passes through (0,-6) and (8,0)
y = -3/4 x + 6 has y intercept +6 and x intercept is +8. So the line passes through (0,6) and (8,0)
y = -3/4 x - 6 has y intercept -6 and x intercept is -8. So the line passes through (0,-6) and (-8,0)
You will see that the quadrilateral is a rhombus. One might be tempted to take it as square as all sides are equal but if you look at the diagonals,
you can find that they are unequal. So it must be a rhombus.
Area of rhombus = (d1 * d2) /2 = (12 * 16)/2 = 96
Answer C
See attached figure.
y = 3/4 x + 6 has y intercept 6 and x intercept is -8(put y =0 in the equation and calculate for x). So the line passes through (0,6) and (-8,0)
y = 3/4 x - 6 has y intercept -6 and x intercept is 8. So the line passes through (0,-6) and (8,0)
y = -3/4 x + 6 has y intercept +6 and x intercept is +8. So the line passes through (0,6) and (8,0)
y = -3/4 x - 6 has y intercept -6 and x intercept is -8. So the line passes through (0,-6) and (-8,0)
You will see that the quadrilateral is a rhombus. One might be tempted to take it as square as all sides are equal but if you look at the diagonals,
you can find that they are unequal. So it must be a rhombus.
Area of rhombus = (d1 * d2) /2 = (12 * 16)/2 = 96
Answer C
Attachments
rhombus.jpg [ 47.46 KiB | Viewed 15299 times ]
General Discussion
08 Jun 2015, 04:26
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Bunuel
MANHATTAN GMAT OFFICIAL SOLUTION:
All of these line equations are of the form y = mx + b, where m is the slope and b is the y-intercept. Two of these lines have a slope of 3/4 and are thus parallel to each other. The other two lines are parallel to one another with a slope of –3/4. Two of the lines have a y-intercept of 6 while the other two lines have a y-intercept of –6.
Sketch the lines:
In each quadrant, we have a triangle with the dimensions 6–8–10, a multiple of the common 3–4–5 right triangle:
Area = 4(1/2*bh) = 2bh = 2*6*8 = 96.
Alternatively, recognize that the quadrilateral is a rhombus (four equal sides of length 10), and use the formula for the area of a rhombus: \(\frac{D_1*D_2}{2}\), where D indicates the length of the diagonals:
The correct answer is C.
Attachment:
2015-06-08_1520.png [ 76.84 KiB | Viewed 15615 times ]
