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Lines k and m are parallel to each other. Is the slope of

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Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 05 Sep 2010, 06:55
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Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).
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Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 05 Sep 2010, 07:14
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Orange08 wrote:
Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


It's straight E.

The best way to solve this problem is to visualize it. We have line k, which passes through the point (3, 2) and its parallel line m, which passes through the point (-3,2). If you draw one such pair and fix, then you can rotate them 360 degrees to get infinite number of lines with negative as well positive slopes.

Answer: E.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Re: Slope of one of the parallel lines  [#permalink]

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New post 08 Sep 2010, 10:13
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Orange08 wrote:
Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


To find a slope we need at least 2 points on a line. Here only one point is given for each line.
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 08 Feb 2016, 19:10
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


In the original condition, there are 4 variables(x1, x2, y1, y2) from the slope=(y2-y1)/(x2-x1). (There are 2 lines, which makes 8 variables. However, since the lines are parallel, which makes 4 variables) In order to match with the number of equations, you need 4 equations, which is likely to make E the answer.
When 1) & 2), you cannot figure out the slope of either line k or line m in a unique way, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 27 Aug 2016, 13:05
Can you please explain why 4 variables in case of parallel lines and not 8

Thanks

MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


In the original condition, there are 4 variables(x1, x2, y1, y2) from the slope=(y2-y1)/(x2-x1). (There are 2 lines, which makes 8 variables. However, since the lines are parallel, which makes 4 variables) In order to match with the number of equations, you need 4 equations, which is likely to make E the answer.
When 1) & 2), you cannot figure out the slope of either line k or line m in a unique way, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 27 Aug 2016, 23:45
parthasd wrote:
Can you please explain why 4 variables in case of parallel lines and not 8

Thanks

MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


In the original condition, there are 4 variables(x1, x2, y1, y2) from the slope=(y2-y1)/(x2-x1). (There are 2 lines, which makes 8 variables. However, since the lines are parallel, which makes 4 variables) In order to match with the number of equations, you need 4 equations, which is likely to make E the answer.
When 1) & 2), you cannot figure out the slope of either line k or line m in a unique way, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.


4 variables in case of || lines because ||lines always have an equal slope. So, once you find the slope of 1 line, you don't need to find the slope of another line separately.
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Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 16 Jul 2017, 23:17
If i go by the defination of parallel lines : Parallel lines are two lines that are always the same distance apart and never touch.

if i take into consideration both option then both lines have a common intercept on Y-axis that is 2 so how come the two lines are parallel to each other ?
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 16 Jul 2017, 23:29
kunalsingh1991 wrote:
If i go by the defination of parallel lines : Parallel lines are two lines that are always the same distance apart and never touch.

if i take into consideration both option then both lines have a common intercept on Y-axis that is 2 so how come the two lines are parallel to each other ?


One of the infinitely many possible cases is given below:
Image

If you rotate both lines simultaneously you'll get other cases.

Attachment:
Untitled.png
Untitled.png [ 9.6 KiB | Viewed 3894 times ]

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Lines k and m are parallel to each other. Is the slope of  [#permalink]

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Orange08 wrote:
Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


Target question: Is the slope of line k positive?

Given: Lines k and m are parallel to each other.

Let's jump straight to....

Statements 1 and 2 combined
There are many cases that satisfy BOTH statements. Here are two:

Case a:
Image
In this case, the slope of line k is POSITIVE


Case b:

Image
In this case, the slope of line k is NEGATIVE

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:

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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 01 Aug 2017, 09:40
Bunuel wrote:
Orange08 wrote:
Lines k and m are parallel to each other. Is the slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


It's straight E.

The best way to solve this problem is to visualize it. We have line k, which passes through the point (3, 2) and its parallel line m, which passes through the point (-3,2). If you draw one such pair and fix, then you can rotate them 360 degrees to get infinite number of lines with negative as well positive slopes.

Answer: E.

For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.


I was going through the GMAT Math book and found concept of slope- As per my understanding of the slope concept, if the x & y co-ordinates both have the same sign, we can say that the line has a negative slope. Also when X & Y co-ordinates have opposite sign, we can say that the slope is positive.

In the question, from 1, we are getting K passes through (3,2) i.e. both positive, hence its slope should be negative. Isn't it?

Pls help I am having a tough time with co-ordinate geometry and it would be great if you could clarify the concept of slope for me.

Thanks
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 21 Aug 2017, 10:18
Ive a silly question but would appreciate a reply.

The slope of a line is also equal to -coefficient of x/ coefficient of y. Since the slopes of x and y are equal, arent the two points enough to answer the question?
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 18 Sep 2017, 02:46
m = (y2- y1)/(x2-x1) . Thus co-ordinates of two points must be known to find the slope
1. co-ordinate of only 1 point is known. Not sufficient
2. co-ordinate of only 1 point is known. Not sufficient
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 23 Sep 2017, 23:04
Hello manasvinimehta1@gmail.com

Welcome to GMAT Club!

You are right the slope of the two lines are same. Thats because they are both parallel. But the question asks if the slope of the lines is Positive. How do we know if the slope of both lines is +ve/both -ve/both zero/both infinite?

With both the given information, its impossible to know. Hence the answer is E for this. Others user above have given detailed reply for this.



manasvinimehta1@gmail.com wrote:
Ive a silly question but would appreciate a reply.

The slope of a line is also equal to -coefficient of x/ coefficient of y. Since the slopes of x and y are equal, arent the two points enough to answer the question?

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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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New post 20 Dec 2017, 07:52
Orange08 wrote:
Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


We are given that lines k and m are parallel to each other, and when two lines are parallel, they have the same slope. We must determine whether the slope of line k is positive.

Statement One Alone:

Line k passes through the point (3, 2).

Using the information in statement one, the slope of line k can be positive or negative. An infinite number of lines can pass through the point (3, 2), some of which have positive slopes and some of which have negative slopes. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Line m passes through the point (-3, 2).

Using the information in statement two, we know that the slope of line m can be positive or negative. An infinite number of lines can pass through the point (-3, 2), some of which have positive slopes and some of which have negative slopes. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know that line k passes through (3, 2) and line m passes through (-3, 2). However, we still do not have enough information to determine whether the slope of line k is positive or negative, since both lines can have positive slopes or both can have negative slopes.
Thus, statements one and two together are not sufficient to answer the question.

Answer: E
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Re: Lines k and m are parallel to each other. Is the slope of &nbs [#permalink] 20 Dec 2017, 07:52
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