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GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 If m represents the slope of a line in the coordinate geom  [#permalink]

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Question Stats: 49% (01:30) correct 51% (01:23) wrong based on 370 sessions

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If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
2. $$m^2=3m$$

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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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gmatpapa wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
2. $$m^2=3m$$

Theory:
1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

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PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62[/textarea]
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient
##### General Discussion
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Two questions:

First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants?

Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer?

Thanks!
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. |m|= m
M>=0

The slope could be equal to zero in which case the line runs flat along the x axis and does not pass through QIII.

The slope could be equal to 5 in which case the line would pass through QIII at some point.
INSUFFICIENT

2. m^2=3m

M^2 - 3m = 0

m=0, m=3. As with above, if m=0 it will not pass through QIII but if m=3 then it will.
INSUFFICIENT

1+2
#1 tells us m>=0 and #2 tells us m=0 OR m=3 which is redundant when considering #1. Therefore, m may or may not pass through QIII.
INSUFFICIENT

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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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WholeLottaLove wrote:
Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Two questions:

First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants?

Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer?

Thanks!

Next, when considering the statements we have that m=0, which means that the line is horizontal. The question is "does the line intersect quadrant III?" not what is the value of m. Horizontal line may or may not intersect quadrant III.

Hope it's clear.
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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WholeLottaLove wrote:
Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Two questions:

First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants?

Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer?

Thanks!

I think you are confusing the parts of the equation of the line.
$$y=Slope(=m)*X+k$$<== this is the standard for of a line.

These two lines have NO SLOPE (they are straight, horizontal, parallel to the x-axis) => m=0.
$$y=-100$$ $$y=100$$. y=-100 is a straight line that passes through the III and IV quadrant; y=100 passes through the I and II quadrant.
(refer to the image)

If we know that m=0 both y=100 and y=-100 are still valid.
Attachments Im.JPG [ 12.14 KiB | Viewed 11827 times ]

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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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Bunuel wrote:
WholeLottaLove wrote:
Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Two questions:

First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants?

Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer?

Thanks!

Next, when considering the statements we have that m=0, which means that the line is horizontal. The question is "does the line intersect quadrant III?" not what is the value of m. Horizontal line may or may not intersect quadrant III.

Hope it's clear.

Ahhh. It's been a while since I've done anything related to coordinate geometry (trying to nail modules down cold haha!) Now I remember. Thanks.
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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This is an updated version of my original solution found above.

If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. |m|= m
M>=0

If m = 0 then it has no slope. However, it still may or may not pass through QIII. If y = 2 then it would be a flat line passing through QI and QII. If y = -2 then it would be a flat line passing through QIII and QIV. Furthermore, if the line did have a slope, it may or may not pass through QIII. For example, if it had a slope of 2 it would pass through QIII (assuming it has infinite length) but if the slope was negative it may not ever pass through QIII)
INSUFFICIENT

2. m^2=3m

M^2 - 3m = 0

m=0, m=3. If the slope is zero then it may or may not pass through QIII. We would need to know it's y coordinate to determine that. If the slope is positive 3, then it would pass through QIII
INSUFFICIENT

1+2
Both 1 and 2 tell us that the slope could be zero or greater than zero. If the slope is zero then it may or may not pass through QIII. If it is greater than zero it will. We cannot determine if it passes through QIII or not.
INSUFFICIENT

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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Hi Zarrolou,

St1 |m|= m can also be inferred as |-m|=|m|= m since |-m|=|m|

this implies m>/ 0 or m <0

Combining with statement 2 we get m=0 as common and again answer can be yes or no depending upon value of y.

Will the above interpretation of st1 will be correct.

thanks
Mridul
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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mridulparashar1 wrote:
Zarrolou wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
So m is $$\geq{ 0}$$. If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider $$y=-100$$ (yes) and $$y=100$$ (no)

2. $$m^2=3m$$
$$m^2-3m=0$$ so $$m=3$$ or $$m=0$$. If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2) Since m=0 is common, both statements are still not sufficient

Hi Zarrolou,

St1 |m|= m can also be inferred as |-m|=|m|= m since |-m|=|m|

this implies m>/ 0 or m <0

Combining with statement 2 we get m=0 as common and again answer can be yes or no depending upon value of y.

Will the above interpretation of st1 will be correct.

thanks
Mridul

No, that's not correct.

$$|m|=m$$ implies that $$m\geq{0}$$ ONLY. What does m>/ 0 or m <0 even mean? It gives all values possible, doesn't it?

Absolute value properties:

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$.
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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My 2 cents for this long discussion.
statement 1= |M|=M
in this case m can be 0 or +ve or -ve
NS

Statement 2= m^2=3m
hence m can be 3 or 0 NS

Combining M can be +ve or 0 thus E is the correct answer.
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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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gmatpapa wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
2. $$m^2=3m$$

Statement 1. $$|m|= m$$
Analyzing the modulus : |Any number|= either 0 or +
That implies the value of m can be either 0 or +
Now if the slope of a line is either 0 or +, it can intersect or not intersect Quadrant III.
As Slope = Change in y/change in X
Scenario A: if ^y =+ and ^X=+, slope =+ ; Slope will intersect
Scenario B: if ^y =- and ^X=-, slope =+ ; Slope will intersect
Scenario C: if ^y =0 and ^X=-, slope =0 ; Slope will not intersect

So, It is not sufficient.

Statement 2. $$m^2=3m$$[/quote]
This statement also implies m is either + or 0 as product of a positive no. and a variable is equal to a square number.
Therefore again it is a restatement of earlier 1. So, It is also not sufficient.

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Re: If m represents the slope of a line in the coordinate geom  [#permalink]

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gmatpapa wrote:
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. $$|m|= m$$
2. $$m^2=3m$$

Target question: Does the line intersect quadrant III?
Jump straight to...

Statements 1 and 2 combined
Here are two scenarios that satisfy BOTH statements:
Case a: m = 3 In this case, the answer to the target question is YES, the line DOES intersect quadrant III

Case b: m = 0. In this case, the answer to the target question is NO, the line does NOT intersect quadrant III

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

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