coordinate geometry

AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Wed Jun 18, 2008 9:49 am

The question is asking you whether the line is going to pass through quadrant II.

The first statement tells you that line K has a negative slope:

Up 1 and over 6 to the left, down 1 and over 6 to the right.

You might then think to yourself, "Well, I don't know from which point the line starts, what if it's somewhere off the chart provided here...hmmm, I know!! I need a y-intercept!" However, you do not need the y-intercept because, as durgesh pointed out, any line with a negative slope will pass through quadrant II.

Statement 1 is sufficient.

The second statement tells you that the y-intercept is -6. So start at the origin (0) and move down along the y-axis to -6. Great! The line passes through this point, but does it go from QI to Q III or Q IV to QII?? Now, if only you had the slope of the line you would be able to plot the points of the line and see if it passes through the second quadrant. So, again, you might think that you need the above statement. But, you do not. Statement 1 alone is enough.

https://second-lap.blocked/

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rishi235: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Aug 02, 2008 10:05 pm; Thanked: 5 times

Hi AleKsandrM

by rishi235 » Sat Aug 16, 2008 11:56 am

Hi AleKsandrM
In ur explanation, u sed that

"The first statement tells you that line K has a negative slope:
Up 1 and over 6 to the left, down 1 and over 6 to the right."

I understood this wrt 2 above problem.
But I'm facing problems using this technique 4 another prob

With Up 1 and over 6 to the left - Do u mean that the line K passes through (1,0) AND (0,-6) or do u mean that line K passes thru (1,-6)

Please clear this funda 4 me...Wud me of great help to me...\

Thanks
Rishi

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Sat Aug 16, 2008 1:59 pm

Well, I don't really know if the line passes through (1, -6), or through (-1, 6) for that matter. What I DO know, is that if you keep going from a given point at the increments which the slope indicates, you will eventually get to quadrant II. Remember, a line goes on and on. If someone tells you that they are talking about line AB, what they really mean is line SEGMENT AB, since the line keeps going in either direction. Therefore, you follow the line from any intercept, and go up 1 and over 6 to the left, and up 1 and over 6, up 1 and over 6....however many steps it takes, you will eventually follow the line into the second quadrant. Hope this is clear.

https://second-lap.blocked/

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rishi235: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Aug 02, 2008 10:05 pm; Thanked: 5 times

Thanks AleksanrM...

by rishi235 » Sat Aug 16, 2008 8:46 pm

Thanks AleksanrM...
I definitely got the funda for this problem. But I was trying to use this technique in another problem as below:

Lines n & p lie in the xy-plane. Is the slope of line n less than the slope of line p?
1) Lines n & p intersect at the point (5,1)
2) The y-intercept of line n is greater than the y-intercept of line p.

This problem has already been discussed in another thread but not with this technique. The discussion link for this problem is given below 4 ur reference:
https://www.beatthegmat.com/ds-coordinat ... t7351.html

So my issue is whether we use the technique u mentioned in this problem?

Thanks
Rishi

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Sun Aug 17, 2008 7:21 am

Not really. This problem is different in that it compares two slopes. We don't really care about the actual slope. We only care about the possible relationship between the slopes of two lines. In this problem, if you draw a coordinate plane, you will see that the first statement does not provide you with any useful information on its own.

The second statement may look as if it's enough to answer the question. You draw the two lines and see that the y-intercept is greater, so there you go, you can answer the question. However, you cannot. You can have three possibilities:

1) The slope of line n is negative and slope of line p is positive, in which case they will intersect in quadrant IV and slope n < slope p.

2) The slope of line n is positive and the slope of line P is negative, in which case they will intersect in quadrant III and slop p < slope n.

3) The two lines are parallel, in which case slope p = slope n.

What you need to know is whether and where the two lines intersect. You are provided with that information in statement one. Therefore, you need both statements to answer this question.

https://second-lap.blocked/