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11 Feb 2023, 23:09
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Difficulty:
65%
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Question Stats:
53% (02:16) correct
47%
(02:12)
wrong
based on 83
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In the diagram, the line connecting A and B has slope of -2 and the y-coordinate of A is a positive number. Is the area of the triangle created by the points A, B, and O greater than 25 ?
(1) The x-coordinate of B is less than 7.
(2) The y-coordinate of A is greater than 11.
Attachment:
2023-02-12_10-08-50.png [ 9.03 KiB | Viewed 2455 times ]
12 Feb 2023, 00:33
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Option B
Statement 1 gives us that base of the triangle is <7. Since the slope is -2, the height would be y coordinate of A will be <14. Therefore the area of the triangle will be less than 0.5*7*14=49. So the area is less than 49. Not sufficient to tell us whether it is greater than 25
Statement 2 gives us that height of the triangle (y coordinate of A) is greater than 11. So x coordinate of B will be greater than 5.5. So minimum area = 0.5* 11*5.5 = 30.25. Which is greater than 25. So Sufficient
Statement 1 gives us that base of the triangle is <7. Since the slope is -2, the height would be y coordinate of A will be <14. Therefore the area of the triangle will be less than 0.5*7*14=49. So the area is less than 49. Not sufficient to tell us whether it is greater than 25
Statement 2 gives us that height of the triangle (y coordinate of A) is greater than 11. So x coordinate of B will be greater than 5.5. So minimum area = 0.5* 11*5.5 = 30.25. Which is greater than 25. So Sufficient
12 Feb 2023, 03:02
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Bunuel
Area of the triangle AOB = \(\frac{1}{2}\) OA * OB
Statement 1
(1) The x-coordinate of B is less than 7.
Area of the triangle when B = (7,0)
Equation of AB ⇒
\(y - y_1 = m (x - x_1) \)
\(y - 0 = -2 (x - 7) \)
y intercept ⇒ y = 14
Area of the triangle = 1/2 * 14 * 7 = 49 units^2
However, given that the x-coordinate of B is less than 7, the line AB can be any point towards the origin. The area of the triangle hence will be less than 49 sq. units. However, at some value of B, the area will be greater than 25 and for some value, the area will be less than 25.
The area of the triangle becomes smaller as we move line AB closer to the origin.
Attachment:
Option A.jpg [ 8.68 KiB | Viewed 1728 times ]
Statement 2
(2) The y-coordinate of A is greater than 11.
Area of the triangle when A = (0,11)
Equation of AB ⇒
\(y - y_1 = m (x - x_1) \)
\(y - 11 = -2 (x - 0) \)
x intercept ⇒ y = 11/2
Area of the triangle = 1/2 * 11/2 * 11 = 121/4 units^2 ⇒ i.e. greater than 30 sq.units
However, given that the x-coordinate of A is greater than 11, the line AB will be above the line when y coordinate is 11. Hence the area of the triangle will always be greater than 30 sq. units.
Attachment:
Option B.jpg [ 10.38 KiB | Viewed 1698 times ]
Hence the statement is sufficient.
Option B
