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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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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).
[Reveal] Spoiler: OA
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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 07 Sep 2010, 23:20
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Re: Slope of one of the parallel lines [#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).


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

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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
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] 27 Aug 2016, 23:45
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