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19 Jul 2019, 01:03
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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:
5%
(low)
Question Stats:
85% (01:12) correct
15%
(01:14)
wrong
based on 239
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A, B, and C are three points on the line shown in the figure. In the figure, is t equal to 55?
(1) A = (25, 50)
(2) B = (35, 60)
Attachment:
2019-07-19_1201.png [ 26.48 KiB | Viewed 5185 times ]
19 Jul 2019, 10:52
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In this question, the slope concept can be utilized to establish an equation, since the three points A, B and C lie on the same line.
This means, Slope of CA = Slope of BC
If the co-ordinates of two points are (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)), then the slope of the line connecting these points is given by \(\frac{(y_2 – y_1)}{(x_2 – x_1)}\).
Let the co-ordinates of point A be (25, a) and the co-ordinates of point B be (35, b). Then,
Slope of CA = \(\frac{(t-a)}{(30 – 25)}\) = \(\frac{(t-a)}{5}\) and
Slope of BC = \(\frac{(b-t)}{(35 – 30)}\) = \(\frac{(b-t)}{5}\).
Since slope of CA = slope of BC, we can say (t-a) = (b-t). This means,
t = \(\frac{(a+b)}{2}\).
To find out if t is equal to 55, we need the values of both a and b. Clearly, these are given in the individual statements.
Therefore, neither statement I alone nor statement II alone is sufficient to answer the question. Answer options A, B and D can be eliminated.
We see that, when we combine the statements, we get the value of a = 50 and b = 60. Plugging in these values in the equation for t, we see that t = 55.
We can answer the question with a definite Yes. Combination of statements is sufficient.
The correct answer option is C.
In a question like this, analyzing the question data is important, especially when such a clear diagram is given which gives you lot of data. Assuming the co-ordinates for A and B is equally important because it gives you a chance to develop an equation.
Analysing the question stem will give you an equation/expression/inequality, which will tell you what is the data that you have to look for in the statements. This will take almost the same time as trying out the individual statements, but will help you build a habit of analyzing the question stems, which will in turn help you in the tougher questions.
Hope this helps
This means, Slope of CA = Slope of BC
If the co-ordinates of two points are (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)), then the slope of the line connecting these points is given by \(\frac{(y_2 – y_1)}{(x_2 – x_1)}\).
Let the co-ordinates of point A be (25, a) and the co-ordinates of point B be (35, b). Then,
Slope of CA = \(\frac{(t-a)}{(30 – 25)}\) = \(\frac{(t-a)}{5}\) and
Slope of BC = \(\frac{(b-t)}{(35 – 30)}\) = \(\frac{(b-t)}{5}\).
Since slope of CA = slope of BC, we can say (t-a) = (b-t). This means,
t = \(\frac{(a+b)}{2}\).
To find out if t is equal to 55, we need the values of both a and b. Clearly, these are given in the individual statements.
Therefore, neither statement I alone nor statement II alone is sufficient to answer the question. Answer options A, B and D can be eliminated.
We see that, when we combine the statements, we get the value of a = 50 and b = 60. Plugging in these values in the equation for t, we see that t = 55.
We can answer the question with a definite Yes. Combination of statements is sufficient.
The correct answer option is C.
In a question like this, analyzing the question data is important, especially when such a clear diagram is given which gives you lot of data. Assuming the co-ordinates for A and B is equally important because it gives you a chance to develop an equation.
Analysing the question stem will give you an equation/expression/inequality, which will tell you what is the data that you have to look for in the statements. This will take almost the same time as trying out the individual statements, but will help you build a habit of analyzing the question stems, which will in turn help you in the tougher questions.
Hope this helps
20 Jul 2019, 16:46
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If we know only one point on the line, that line can rotate in any direction in the plane. We need atleast 2 points to fix a line in the plane or to define the equation of the line.
Hence statement 1 and 2 are insufficient, as they give co-ordinates of only one point on the line. By combining 2 statements, we get 2 distinct points on the line. now we can find any property of that line or any point on that line.
C
Hence statement 1 and 2 are insufficient, as they give co-ordinates of only one point on the line. By combining 2 statements, we get 2 distinct points on the line. now we can find any property of that line or any point on that line.
C
Bunuel
