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In the xyplane is the slope of line k equal to 0? [#permalink]
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In the xyplane is the slope of line k equal to 0? (1) The xintercept of k is 0. (2) The yintercept of k is 0.
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Re: In the xyplance is the slope of line k equal to 0? [#permalink]
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fozzzy wrote: In the xyplance is the slope of line k equal to 0?
1) the xintercept of k is 0 2) the yintercept of k is 0. The question is asking whether the link k is parallel to xaxis or xaxis 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 xyplance is the slope of line k equal to 0? [#permalink]
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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 xyplane 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: mathcoordinategeometry87652.html). (1) The xintercept of k is 0. Now, I'm not a verbal expert, but the xintercept implies that there is only one point of interception with xaxis, which means that we can eliminate y=0 line. So, we have that line k is not y=0 and has xintercept, thus it cannot be horizontal > the slope does not equal to 0. Sufficient. (2) The yintercept of k is 0. Clearly insufficient. Answer: A. I think GMAT Prep is wrong here.
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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29 Dec 2013, 00:46
fozzzy wrote: In the xyplane is the slope of line k equal to 0?
(1) The xintercept of k is 0. (2) The yintercept of k is 0. (1) xintercept of a line is the distance of the origin from the point where the line cuts xaxis...x intercept 0 means the distance is 0, i.e. the line passes through the origin. You cannot say anything about the slope. (2) yintercept of a line is the distance of the origin from the point where the line cuts yaxis...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



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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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01 Apr 2014, 08:21
goodyear2013 wrote: Hi, I emailed the GMAC and checked the answer of this question. I asked whether the answer could be (A).
Here is the reply of GMAC;
Answer is E. The answer explanation explains it. There are an infinite number of equations that have an xintercept = 0 but do not have a slope equal to 0. The answer explanation provides just one counter example: the equation y=x. Other counterexamples include y=2x, y=3x, y=1/2x, y=1/3x, etc. Because there is at least one example where the answer is yes (the slope = 0) and at least one example where the answer is no (the slope is not = 0), then statement (1) is not sufficient. None of the examples from GMAC (y=x, y=2x, y=3x, y=1/2x, y=1/3x) has the slope of 0. They say " an xintercept = 0", while the question says " the xintercept of k is 0". In the current form the answer must be A, no matter what the GMAC says.
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Re: In the xyplance is the slope of line k equal to 0? [#permalink]
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07 Sep 2013, 14:25
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Marcab wrote: fozzzy wrote: In the xyplance is the slope of line k equal to 0?
1) the xintercept of k is 0 2) the yintercept of k is 0. The question is asking whether the link k is parallel to xaxis or xaxis 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. Comments are appreciated.



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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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27 Sep 2013, 01:21
gmatter0913 wrote: Xintercept 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 coordinate axes only at the origin)
The equation of the line is: y  0 = (20)/(20) * (x0) This leads to the equation x=y
What is the xintercept of this line? It is zero. Because it crosses the Xaxis at 0. What is the yintercept of this line? It is zero. Because it crosses the Yaxis at 0.
What is the slope of this line? 45 degrees
A line can have a slope even if its Xintercept is zero. Because it passes through the origin.
The OA explanation says exactly that. If the Xintercept is zero, the line can be of the form y=x or y=0
Hence the answer is E The OE is not correct.
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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Re: In the xyplance is the slope of line k equal to 0? [#permalink]
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21 Jan 2013, 04:50
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 xyplane is the slope of line k equal to 0? [#permalink]
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21 Jan 2013, 05:14
The official explanation
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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In the xyplane, is the slope of line k equal to 0 ? [#permalink]
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25 Apr 2013, 17:43
In the xyplane, is the slope of line k equal to 0 ? (1) The xintercept of k is 0. (2) The yintercept 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 xaxis because it is on the x axis. Therefore, there would be infinite xintercepts, 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 xyplane, is the slope of line k equal to 0 ? [#permalink]
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26 Apr 2013, 00:18
danzig wrote: In the xyplane, is the slope of line k equal to 0 ? (1) The xintercept of k is 0. (2) The yintercept 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 xaxis because it is on the x axis. Therefore, there would be infinite xintercepts, 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 xyplane is the slope of line k equal to 0? [#permalink]
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27 Apr 2013, 10:42
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 xyplane is the slope of line k equal to 0? [#permalink]
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28 Apr 2013, 03:22



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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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09 Sep 2013, 14:02
Let me give it a try: In the xyplane is the slope of line k equal to 0? (1) The xintercept of k is 0. (2) The yintercept 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. Answer should be E. Kindly prove it graphically if you have any different concept.
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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10 Sep 2013, 01:34
PiyushK wrote: Let me give it a try: In the xyplane is the slope of line k equal to 0? (1) The xintercept of k is 0. (2) The yintercept 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. Answer should be E. Kindly prove it graphically if you have any different concept. THe correct answer is A, not E. Check here: inthexyplaneistheslopeoflinekequalto146084.html#p1171693
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Re: In the xyplane is the slope of line k equal to 0? [#permalink]
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10 Sep 2013, 04:33
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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