Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 Aug 2014
Posts: 15
Location: United States
Concentration: Human Resources, General Management
GPA: 3.97
WE: Information Technology (Insurance)

Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
Updated on: 10 Apr 2016, 09:51
Question Stats:
59% (00:38) correct 41% (00:50) wrong based on 649 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by surupab on 10 Apr 2016, 08:38.
Last edited by Bunuel on 10 Apr 2016, 09:51, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Aug 2009
Posts: 6258

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
10 Apr 2016, 09:00
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
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




Senior Manager
Joined: 18 Jan 2010
Posts: 254

Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
22 May 2016, 23:00
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. )




Manager
Joined: 17 Oct 2015
Posts: 111
Location: India
Concentration: Finance
GMAT 1: 690 Q47 V37 GMAT 2: 700 Q44 V41
WE: Corporate Finance (Commercial Banking)

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
10 Apr 2016, 11:06
i chose E which, i now realize is wrong. Great solution chetan2u sir. Concept got clear.



Manager
Joined: 12 Jan 2015
Posts: 210

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
13 Apr 2016, 23:55
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.
_________________
Thanks and Regards, Prakhar



Math Expert
Joined: 02 Aug 2009
Posts: 6258

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
14 Apr 2016, 00:05
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...
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Current Student
Joined: 28 Nov 2014
Posts: 891
Concentration: Strategy
GPA: 3.71

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
26 Aug 2016, 13:51
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?



Manager
Joined: 03 Jul 2016
Posts: 76

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
26 Aug 2016, 14:17
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.



Intern
Joined: 24 Aug 2016
Posts: 29

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
09 Sep 2016, 00:15
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.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
11 Sep 2016, 06:12
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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 27 Mar 2016
Posts: 24
Location: India
Concentration: Entrepreneurship, Social Entrepreneurship
WE: General Management (Consumer Products)

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
07 Oct 2016, 07:54
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



Current Student
Joined: 28 Nov 2014
Posts: 891
Concentration: Strategy
GPA: 3.71

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
09 Oct 2016, 03:13
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



Manager
Joined: 13 Dec 2013
Posts: 161
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
06 Apr 2017, 20:35
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.



Intern
Joined: 17 May 2016
Posts: 15
Location: United States

Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
04 Aug 2017, 02:04
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?



Intern
Joined: 29 Jul 2012
Posts: 15

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
16 Sep 2017, 00:21
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



Manager
Joined: 26 Jan 2016
Posts: 60
Location: India
Concentration: General Management, Statistics
GMAT 1: 670 Q49 V31 GMAT 2: 730 Q49 V41
GPA: 3
WE: Information Technology (Computer Software)

Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
01 Oct 2017, 07:02
Ohh it was simple, I chose E. I didn't understand in the first place what exactly "cross" mean. Never used "cross" for "intersect" .



Intern
Joined: 09 Sep 2017
Posts: 5

Re: Does the line with equation ax+by = c, where a,b and c are real consta
[#permalink]
Show Tags
01 Oct 2017, 08:38
[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.
[size=80][b][i]Posted from my mobile device[/i][/b][/size]




Re: Does the line with equation ax+by = c, where a,b and c are real consta &nbs
[#permalink]
01 Oct 2017, 08:38






