If the point (4,6) lies on line l, and the point (x,3)

Question

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.

mittalg · Answer

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!!!

WoundedTiger · Answer

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

gauravsoni · Answer

Thanks WoundedTiger,

good explanation, i do have to brush up the coordinate geometry, really weak at it.

Bunuel · Answer

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?

So, we have one point of the line, (4,6), and know that it intersects with line y=3 at some point. We need to find x-coordinate of the intersection point.

(1) l passes through (0,0). We are given second point of the line, which means that the line is fixed, completely defined. We can find anything we want about that line. Sufficient.

(2) The slope of line l is positive. A line with positive slope passing through (4, 6) can have different intersection points with y=3. Not sufficient.

Answer: A.

Remember, on DS problems, all you need to do is evaluate whether you would be able to arrive at the answer using the information provided in each statement; you don’t need to waste time actually finding the answer.

Bunuel · Answer

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

If the point (4,6) lies on line l, and the point (x,3)

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If the point (4,6) lies on line l, and the point (x,3)

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