In the xy-plane is the slope of line k equal to 0? : GMAT Data Sufficiency (DS)
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# In the xy-plane is the slope of line k equal to 0?

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In the xy-plane is the slope of line k equal to 0? [#permalink]

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20 Jan 2013, 06:09
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In the xy-plane is the slope of line k equal to 0?

(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.
[Reveal] Spoiler: OA

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Last edited by fozzzy on 18 Jun 2013, 00:37, edited 1 time in total.
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Re: In the xy-plance is the slope of line k equal to 0? [#permalink]

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20 Jan 2013, 07:25
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fozzzy wrote:
In the xy-plance is the slope of line k equal to 0?

1) the x-intercept of k is 0
2) the y-intercept of k is 0.

The question is asking whether the link k is parallel to x-axis or x-axis itself.

1) x intercept of k =0
i.e. when line k intersects x axis, the intersection point is at 0 distance from origin OR indirectly the line k intersects x axis at origin.
Insufficient infromation as the line can have any slope.

2) y intercept of k=0
i.e. when line k intersects y axis, the intersection point is at 0 distance from origin OR indirectly the line k intersects y axis at origin.
Insufficient info as the line can have any slope.

On combining, we see that the line passes through origin.
Now we see that the line can have any slope. The slope can be positive, negative and zero.
Not sufficient.
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Re: In the xy-plance is the slope of line k equal to 0? [#permalink]

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21 Jan 2013, 03:50
Don't you think this question has ambiguity, the official explanation didn't really make sense. Its taking into account multiple intercepts.
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Re: In the xy-plance is the slope of line k equal to 0? [#permalink]

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21 Jan 2013, 04:04
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fozzzy wrote:
Don't you think this question has ambiguity, the official explanation didn't really make sense.

Definitely. Is this question really from GMAT Prep? If so, can you pleas provide OA given there? Thank you.

In the xy-plane is the slope of line k equal to 0?

The questions basically asks whether line k is a horizontal line (the slope of any horizontal line is always zero. For more check here: math-coordinate-geometry-87652.html).

(1) The x-intercept of k is 0. Now, I'm not a verbal expert, but the x-intercept implies that there is only one point of interception with x-axis, which means that we can eliminate y=0 line. So, we have that line k is not y=0 and has x-intercept, thus it cannot be horizontal --> the slope does not equal to 0. Sufficient.

(2) The y-intercept of k is 0. Clearly insufficient.

I think GMAT Prep is wrong here.
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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21 Jan 2013, 04:13
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Here is a screenshot of the question
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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21 Jan 2013, 04:14
The official explanation
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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21 Jan 2013, 04:16
fozzzy wrote:
The official explanation

From my point of view, OA is wrong.
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In the xy-plane, is the slope of line k equal to 0 ? [#permalink]

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25 Apr 2013, 16:43
In the xy-plane, is the slope of line k equal to 0 ?

(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.

My doubt is this:
In (1), $$y = x$$ satisfies the condition, and the answer would be NO.
But if we use $$y = 0$$, it seems that the answer would be YES. However, are we satisfying the condition? I am not sure.
If $$y=0$$, line k is touching every point of the x-axis because it is on the x axis. Therefore, there would be infinite x-intercepts, not only zero. In this sense, $$y=0$$ cannot be a solution, so the slope of line k is not 0. The answer would be NO.
So, (1) would be sufficient.
But the OA is E. Please explain.
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Re: In the xy-plane, is the slope of line k equal to 0 ? [#permalink]

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25 Apr 2013, 23:18
danzig wrote:
In the xy-plane, is the slope of line k equal to 0 ?

(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.

My doubt is this:
In (1), $$y = x$$ satisfies the condition, and the answer would be NO.
But if we use $$y = 0$$, it seems that the answer would be YES. However, are we satisfying the condition? I am not sure.
If $$y=0$$, line k is touching every point of the x-axis because it is on the x axis. Therefore, there would be infinite x-intercepts, not only zero. In this sense, $$y=0$$ cannot be a solution, so the slope of line k is not 0. The answer would be NO.
So, (1) would be sufficient.
But the OA is E. Please explain.

Merging similar topics. Please refer to the solutions above.
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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27 Apr 2013, 09:42
I agree with marcab's solution. As rightly pointed out by marcab and GMat prep solution, a line passing through origin, y = x and say x axis,both have x and y intercept as zero. that is the reason why we write the equation of the point passing through origin as y =mx and not y = mx + c..I don;t think gmat prep solution or marcabs solution is wrong..
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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28 Apr 2013, 02:22
darsh wrote:
I agree with marcab's solution. As rightly pointed out by marcab and GMat prep solution, a line passing through origin, y = x and say x axis,both have x and y intercept as zero. that is the reason why we write the equation of the point passing through origin as y =mx and not y = mx + c..I don;t think gmat prep solution or marcabs solution is wrong..

This is a flawed question from GMAT Prep. The correct answer is A, not E.
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Re: In the xy-plance is the slope of line k equal to 0? [#permalink]

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07 Sep 2013, 13:25
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Marcab wrote:
fozzzy wrote:
In the xy-plance is the slope of line k equal to 0?

1) the x-intercept of k is 0
2) the y-intercept of k is 0.

The question is asking whether the link k is parallel to x-axis or x-axis itself.

1) x intercept of k =0
i.e. when line k intersects x axis, the intersection point is at 0 distance from origin OR indirectly the line k intersects x axis at origin.
Insufficient infromation as the line can have any slope.

2) y intercept of k=0
i.e. when line k intersects y axis, the intersection point is at 0 distance from origin OR indirectly the line k intersects y axis at origin.
Insufficient info as the line can have any slope.

On combining, we see that the line passes through origin.
Now we see that the line can have any slope. The slope can be positive, negative and zero.
Not sufficient.

Ok so I have a another solution, I would appreciate if I could get some comments.

1) x intercept of k =0
If you use y = mx + b, and you apply this condition, you get 0 = mx + b, which is the x intercept of K.
If you reorganize the elements, you get b/m = x. Then, m cannot be 0, because it would be undetermined.
So condition 1 is sufficient.

2) y intercept of k = 0
That just tells you b = 0, but it doesnt say anything about m.

Therefore A is correct.

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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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09 Sep 2013, 13:02
Let me give it a try:

In the xy-plane is the slope of line k equal to 0?
(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.

Y=MX + B standard equation. (check point; ok)

X intercept, theoretical knowledge : A single or multiple points on X axis where curve or line intersects X axis, i.e. at Y=0 for any X intercept.
(http://www.purplemath.com/modules/intrcept.htm)

Data given, X intercept as 0, means line is intersecting X axis at origin, as per above theoretical concept Y must be 0.

Therefore equation becomes.

0=m0+b ==> b=0, clearly we can see that X intercept is (0,0)

Equation of line becomes Y=MX

Now, here slope can take any value, thus we can not tell whether it is zero or not.

Further concept of infinite intercepts caused by overlap of any line over x axis is widely accepted, thus we can consider (0,0) as one of those infinite intercepts.

Kindly prove it graphically if you have any different concept.
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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10 Sep 2013, 00:34
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PiyushK wrote:
Let me give it a try:

In the xy-plane is the slope of line k equal to 0?
(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.

Y=MX + B standard equation. (check point; ok)

X intercept, theoretical knowledge : A single or multiple points on X axis where curve or line intersects X axis, i.e. at Y=0 for any X intercept.
(http://www.purplemath.com/modules/intrcept.htm)

Data given, X intercept as 0, means line is intersecting X axis at origin, as per above theoretical concept Y must be 0.

Therefore equation becomes.

0=m0+b ==> b=0, clearly we can see that X intercept is (0,0)

Equation of line becomes Y=MX

Now, here slope can take any value, thus we can not tell whether it is zero or not.

Further concept of infinite intercepts caused by overlap of any line over x axis is widely accepted, thus we can consider (0,0) as one of those infinite intercepts.

Kindly prove it graphically if you have any different concept.

THe correct answer is A, not E. Check here: in-the-xy-plane-is-the-slope-of-line-k-equal-to-146084.html#p1171693
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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10 Sep 2013, 03:33
Hi,

In my humble opinion the ans should be "e". The exp is not correctly explained.

slope of any line is given by dy/dx (change in y coordinate divided by change in x coordinate)

1) when x intercept is zero, that means y=0 or x=y in this case. So dy/dx = 0 as change in y coordinate is zero.

but in case of y=x; dy/dx = 1 (simple differentiation method) - Insufficient

2) when y intercept is zero that means, x=0 hence dy/dx = (dy/0) {infinite slope} similarly for y=x insufficient

Clearly both statement says the same thing x=0, x=y and y=0
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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10 Sep 2013, 04:36
sayansarkar wrote:
Hi,

In my humble opinion the ans should be "e". The exp is not correctly explained.

slope of any line is given by dy/dx (change in y coordinate divided by change in x coordinate)

1) when x intercept is zero, that means y=0 or x=y in this case. So dy/dx = 0 as change in y coordinate is zero.

but in case of y=x; dy/dx = 1 (simple differentiation method) - Insufficient

2) when y intercept is zero that means, x=0 hence dy/dx = (dy/0) {infinite slope} similarly for y=x insufficient

Clearly both statement says the same thing x=0, x=y and y=0

Not sure I understand what your reasoning but the correct answer is A. Check here: in-the-xy-plane-is-the-slope-of-line-k-equal-to-146084.html#p1171693
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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27 Sep 2013, 00:20
X-intercept of zero doesn't necessarily mean the line is horizontal, it could also mean that the line passes through origin.

Let us take a line passing through the points (2,2) and (0,0). (This line intersects the co-ordinate axes only at the origin)

The equation of the line is: y - 0 = (2-0)/(2-0) * (x-0)
This leads to the equation x=y

What is the x-intercept of this line? It is zero. Because it crosses the X-axis at 0.
What is the y-intercept of this line? It is zero. Because it crosses the Y-axis at 0.

What is the slope of this line? 45 degrees

A line can have a slope even if its X-intercept is zero. Because it passes through the origin.

The OA explanation says exactly that. If the X-intercept is zero, the line can be of the form y=x or y=0

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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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27 Sep 2013, 00:21
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gmatter0913 wrote:
X-intercept of zero doesn't necessarily mean the line is horizontal, it could also mean that the line passes through origin.

Let us take a line passing through the points (2,2) and (0,0). (This line intersects the co-ordinate axes only at the origin)

The equation of the line is: y - 0 = (2-0)/(2-0) * (x-0)
This leads to the equation x=y

What is the x-intercept of this line? It is zero. Because it crosses the X-axis at 0.
What is the y-intercept of this line? It is zero. Because it crosses the Y-axis at 0.

What is the slope of this line? 45 degrees

A line can have a slope even if its X-intercept is zero. Because it passes through the origin.

The OA explanation says exactly that. If the X-intercept is zero, the line can be of the form y=x or y=0

The OE is not correct.
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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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28 Dec 2013, 15:21
Bunuel wrote:
gmatter0913 wrote:
X-intercept of zero doesn't necessarily mean the line is horizontal, it could also mean that the line passes through origin.

Let us take a line passing through the points (2,2) and (0,0). (This line intersects the co-ordinate axes only at the origin)

The equation of the line is: y - 0 = (2-0)/(2-0) * (x-0)
This leads to the equation x=y

What is the x-intercept of this line? It is zero. Because it crosses the X-axis at 0.
What is the y-intercept of this line? It is zero. Because it crosses the Y-axis at 0.

What is the slope of this line? 45 degrees

A line can have a slope even if its X-intercept is zero. Because it passes through the origin.

The OA explanation says exactly that. If the X-intercept is zero, the line can be of the form y=x or y=0

The OE is not correct.

Wow! What on earth was GMAT prep thinking here? Seriously flawed IMHO
Won't study this question at all

@MikeMcGarry what do you think?

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Re: In the xy-plane is the slope of line k equal to 0? [#permalink]

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28 Dec 2013, 23:46
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fozzzy wrote:
In the xy-plane is the slope of line k equal to 0?

(1) The x-intercept of k is 0.
(2) The y-intercept of k is 0.

(1) x-intercept of a line is the distance of the origin from the point where the line cuts x-axis...x intercept 0 means the distance is 0, i.e. the line passes through the origin. You cannot say anything about the slope.

(2) y-intercept of a line is the distance of the origin from the point where the line cuts y-axis...y intercept 0 means the distance is 0, i.e. the line passes through the origin. Here also you cannot say anything about the slope

(1) and (2) both implies the same thing ( the line passes through origin)...you cannot say anything about the slope from both together. hence OA is correct answer is E
Re: In the xy-plane is the slope of line k equal to 0?   [#permalink] 28 Dec 2013, 23:46

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