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Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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10 Apr 2016, 07:38
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Does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis? (1) b not equal to 0 (2) ab>0
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Last edited by Bunuel on 10 Apr 2016, 08:51, edited 1 time in total.
Renamed the topic and edited the question.



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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surupab wrote: does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 Hi, ONLY line that will not cross x axis is the line parallel to x axis... THe equation of line parallel to x axis is y=b.. so if ax+by = c has to be parallel to x axis, a should be 0..lets see the statements.. (1) b not equal to 0This tells us that the line is not parallel to yaxis Insuff (2) ab>0this tells us that neither of a or b is 0.. so the line crosses the xaxis Suff B
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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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10 Apr 2016, 10:06
i chose E which, i now realize is wrong. Great solution chetan2u sir. Concept got clear.



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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13 Apr 2016, 22:55
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Hi chetan2u, I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...? Please assist.
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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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13 Apr 2016, 23:05
PrakharGMAT wrote: Hi chetan2u, I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...? Please assist. Yes, Prakhar the line passing through ORIGIN crosses xaxis at x=0 and yaxis at y=0...
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Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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22 May 2016, 22:00
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Another way:
If line ax+by=c does cross x axis then, there will be a point (z,0) on this line. Which means:
az=c. or z= (c/a). z should have real value and this will be possible when a is not equal to zero.
So our question now becomes: Is a = 0?
statement 1: b not equal to 0; This does not tell anything about a. NS
statement 2: ab>0. a is certainly not equal to 0. Sufficient.
B is the answer.
(Note that if we put z = (c/a) in equation; and we know that a is not equal to zero; we get: (b)(y)=0; Now because statement (2) also says b is not equal to zero, so y will have to be zero. This is what we want and this proves the point that this line cuts x axis. )



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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26 Aug 2016, 12:51
chetan2u wrote: surupab wrote: does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 Hi, ONLY line that will not cross x axis is the line parallel to x axis... THe equation of line parallel to x axis is y=b.. so if ax+by = c has to be parallel to x axis, a should be 0..lets see the statements.. (1) b not equal to 0This tells us that the line is not parallel to yaxis Insuff (2) ab>0this tells us that neither of a or b is 0.. so the line crosses the xaxis Suff B chetan2u My question is wrt Statement A If it is clear that the line is not  to y axis that means the line will be  to x axis? Or can we assume that there is a possibility that the line cuts the x axis and still is not  to y axis?



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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26 Aug 2016, 13:17
Keats wrote: chetan2u wrote: surupab wrote: does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 Hi, ONLY line that will not cross x axis is the line parallel to x axis... THe equation of line parallel to x axis is y=b.. so if ax+by = c has to be parallel to x axis, a should be 0..lets see the statements.. (1) b not equal to 0This tells us that the line is not parallel to yaxis Insuff (2) ab>0this tells us that neither of a or b is 0.. so the line crosses the xaxis Suff B chetan2u My question is wrt Statement A If it is clear that the line is not  to y axis that means the line will be  to x axis? Or can we assume that there is a possibility that the line cuts the x axis and still is not  to y axis? Only a line that is not parallel to both the axes, crosses both the axes at different points or at a single point i.e. origin. Coming to this particular question, as mentioned above, we need to make sure both a and b are not equal to '0' At a point (c/a,0) line becomes by=0. This requires a statement that b is also not equal to '0'. Statement II (ab>0) hints that both a and b are not 0. Hence B.



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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08 Sep 2016, 23:15
PrakharGMAT wrote: Hi chetan2u, I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...? Please assist. This is a really clever thought!! I would say that, in the spirit of the question, to 'cross though an axis' means to have at least 1 value ABOVE the axis and at least 1 value BELOW the axis. Since every value of y=0 exists AT the axis, the line does not pass through it but merely exists AT it infinitely. That is my take anyways. Here is a question: Does y = x^2 pass through the xaxis? I think that it does not, because 100% of it's values are at or above the Xaxis. It has no values below the Xaxis, and therefor it TOUCHES but does not cross? I really don't know, merely speculating.



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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surupab wrote: Does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 We are given a line with equation ax+by = c, where a,b and c are real constants, and we need to determine whether it crosses the xaxis. Let’s start by isolating y in our given equation: ax+by = c by = ax + c y = (a/b)x + (c/b) We now have the given equation in slopeintercept form; the slope is a/b and the yintercept is c/b. Statement One Alone:b not equal to 0 Since we are not provided any information about the slope of the line, statement one is not sufficient. Eliminate answer choices A and D. Statement Two Alone:ab>0 Since ab > 0, neither a nor b can be 0. This means that the slope of the line is not equal to zero. Recall that if the slope of a line is 0, the line is horizontal and will not cross the xaxis unless the line is the xaxis itself. Thus, regardless of the values of a or b, the line will, at some point, cross the xaxis. Answer: B
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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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07 Oct 2016, 06:54
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JeffTargetTestPrep wrote: surupab wrote: Does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 We are given a line with equation ax+by = c, where a,b and c are real constants, and we need to determine whether it crosses the xaxis. Let’s start by isolating y in our given equation: ax+by = c by = ax + c y = (a/b)x + (c/b) We now have the given equation in slopeintercept form; the slope is a/b and the yintercept is c/b. Statement One Alone:b not equal to 0 Since we are not provided any information about the slope of the line, statement one is not sufficient. Eliminate answer choices A and D. Statement Two Alone:ab>0 Since ab > 0, neither a nor b can be 0. This means that the slope of the line is not equal to zero. Recall that if the slope of a line is 0, the line is horizontal and will not cross the xaxis unless the line is the xaxis itself. Thus, regardless of the values of a or b, the line will, at some point, cross the xaxis. Answer: B Perfect. Thanks. I was thinking that if a line passes through Origin, it can't be passing XAxis and accordingly thought I need a solution wherein I can have any nonzero value for YIntercept, but I guess thinking only along the SLOPE Concept helps. Thanks JeffTargetTestPrep



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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09 Oct 2016, 02:13
adiagr wrote: Another way:
If line ax+by=c does cross x axis then, there will be a point (z,0) on this line. Which means:
az=c. or z= (c/a). z should have real value and this will be possible when a is not equal to zero.
So our question now becomes: Is a = 0?
statement 1: b not equal to 0; This does not tell anything about a. NS
statement 2: ab>0. a is certainly not equal to 0. Sufficient.
B is the answer.
(Note that if we put z = (c/a) in equation; and we know that a is not equal to zero; we get: (b)(y)=0; Now because statement (2) also says b is not equal to zero, so y will have to be zero. This is what we want and this proves the point that this line cuts x axis. ) You have done it elegantly and I can make quite some sense out of it. On the first go, I just could not draw conclusions out of these statements. But, your way of reducing the question to checking if a = 0 simplifies the case.Thank You adiagr



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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06 Apr 2017, 19:35
chetan2u wrote: surupab wrote: does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 Hi, ONLY line that will not cross x axis is the line parallel to x axis... THe equation of line parallel to x axis is y=b.. so if ax+by = c has to be parallel to x axis, a should be 0..lets see the statements.. (1) b not equal to 0This tells us that the line is not parallel to yaxis Insuff (2) ab>0this tells us that neither of a or b is 0.. so the line crosses the xaxis Suff B Nice solution! Do you have an idea about what one should know with regard to the general form equation for a straight line (ax+by+c=0)? Only y=mx+c is covered in the OG.



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Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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04 Aug 2017, 01:04
JeffTargetTestPrep wrote: surupab wrote: Does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0 We are given a line with equation ax+by = c, where a,b and c are real constants, and we need to determine whether it crosses the xaxis. Let’s start by isolating y in our given equation: ax+by = c by = ax + c y = (a/b)x + (c/b) We now have the given equation in slopeintercept form; the slope is a/b and the yintercept is c/b. Statement One Alone:b not equal to 0 Since we are not provided any information about the slope of the line, statement one is not sufficient. Eliminate answer choices A and D. Statement Two Alone:ab>0 Since ab > 0, neither a nor b can be 0. This means that the slope of the line is not equal to zero. Recall that if the slope of a line is 0, the line is horizontal and will not cross the xaxis unless the line is the xaxis itself. Thus, regardless of the values of a or b, the line will, at some point, cross the xaxis. Answer: B Hi Jeff, Thank you for explanation, could the formula be parabola and not cross the xaxis?



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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15 Sep 2017, 23:21
Is this the right approach, please comment:
y=(a/b)x+(c/b)
For this line to cross x axis, put y=0 > equation becomes x=c/a and therefore, knowing about a is important, which is satisfied by B



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Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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01 Oct 2017, 06:02
Ohh it was simple, I chose E. I didn't understand in the first place what exactly "cross" mean. Never used "cross" for "intersect" .



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Re: Does the line with equation ax+by = c, where a,b and c are real consta [#permalink]
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01 Oct 2017, 07:38
[quote="surupab"]Does the line with equation ax+by = c, where a,b and c are real constants, cross the xaxis?
(1) b not equal to 0 (2) ab>0[/quote]
If line passes through x axis, the y cordinate at intersection of X axis should be zero. Rewritten, Y = (caX)/b If Y = 0 (caX)/b = 0 Hence, 1. b should not be equal to 0 And caX = 0 X= c/a 2. a should not be equal to 0
From Statement 2 we can see that the product of ab is nit equal to 0, hence we know 1 and 2 are true.
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Re: Does the line with equation ax+by = c, where a,b and c are real consta
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