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Updated on: 08 Dec 2015, 03:34
Originally posted by gauravsoni on 20 May 2014, 12:32.
Last edited by chetan2u on 08 Dec 2015, 03:34, edited 2 times in total.
Last edited by chetan2u on 08 Dec 2015, 03:34, edited 2 times in total.
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A
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If the point (4,6) lies on line l, and the point (x,3) also lies on line l, what is the value of x?
(1) l passes through (0,0).
(2) The slope of line l is positive.
Can someone please explain how to approach such a problem.
(1) l passes through (0,0).
(2) The slope of line l is positive.
Can someone please explain how to approach such a problem.
20 May 2014, 20:34
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gauravsoni
Here is how to approach this problem.
Line passes through two points, (4,6) and (x,3). We have to find the value of x i.e. we have find the coordinates of a point which lie on this line.
What remains contact for a line between any two points is its slope. The slope s here is 6-3/4-x. We can find x, if we can find s from any of the statements
Statement 1: l passes through (0,0). Also, l passes through (4,6). Hence, slope s= 6-0/4-0. Therefore, this statement is sufficient.\
Statement 2: The slope of line l is positive.
This statement just says that s>0 which means 3/4-x>0 or 4-x>0 or x< 4, and nothing beyond this. Hence this is insufficient.
Therefore, we get A as our answer.
Hope it helps!!!
Kudos if you like it!!!
20 May 2014, 20:38
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gauravsoni
Hello Guarav Soni,
We are given that pts (4,6 ) and (x,3) lie on Line L. We need to find x
St 1 tells us that pt(0,0) is also on the line so we can form an equation using the following
\((y-y1)= m(x-x1)\) where \(Slope, m = (y2-y1)/(x2-x1)\)
Since we know that pt (0,0) and (4,6) are on line we can find m = (6-0)/(4-0) or 3/2
Therefore (y-0)= 3/2 (x-0) or\(y=3x/2\)This is the equation of the line
Subsitute y=3 in this equation and you get x= 2
So St 1 is sufficient and option B,C and E can be ruled out here
St 2 tells us that the slope of the line is positive. A positive slope line means it pass through quadrant I and III and there can be multiple values
So St 2 is insufficient.D ruled out
Ans is A
You should brush your knowledge on the subject. A good source will be Gmatclub Math Book. More on this topic can be found here :
math-coordinate-geometry-87652.html
gmat-math-book-in-downloadable-pdf-format-130609.html
