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Manager  Joined: 25 Jul 2010
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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).
Math Expert V
Joined: 02 Sep 2009
Posts: 65785
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).

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.

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

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2
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.

 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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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.

 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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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.

 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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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 ?
Math Expert V
Joined: 02 Sep 2009
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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

Attachment: Untitled.png [ 9.6 KiB | Viewed 15419 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: In this case, the slope of line k is POSITIVE

Case b: 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

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Posts: 69
Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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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.

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

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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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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.

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

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If you imagine this visually, each are lines that pivot around their respective points (3,2) & (-3,2). They could both be rotated by any degree and still be parallel. Hence E since we cannot identify the slope.
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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Tip: Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).

On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.
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Re: 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).

DS12533
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Re: Lines k and m are parallel to each other. Is the slope of  [#permalink]

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Had a conceptual doubt from this question -
- Can we use (x/a)+(y/b)=1, to calculate slope for a line?
- Do we always need 2 points of the line to calculate slope?

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Re: 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).

This needs no math at all

For slope of a line to be positive it must move from left to right upwards only. Like this sign /.

Downward slopy like this \ means negative slope.

By the position of the points in 1) and 2), the lines can slope upwards or downwards and still be parallel.

E.g // or \\
So the heck we can't tell! E is the answer

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

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jeeth1508 wrote:
Had a conceptual doubt from this question -
- Can we use (x/a)+(y/b)=1, to calculate slope for a line?
- Do we always need 2 points of the line to calculate slope?

Yes you need two points to calculate the slope. If you think about it visually, if you just draw a dot on a page, there are infinite straight lines with different slopes that could all go through that point. The moment you put a second dot on the page, there is one unique straight line that will connect those dots and hence you have a known slope.

More generally speaking, to solve a linear equation you need either the slope and a point OR two points.

To solve a quadratic equation, you need either 3 points OR the turning point and one other point. Re: Lines k and m are parallel to each other. Is the slope of   [#permalink] 14 Jun 2020, 05:06

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