Last visit was: 23 Jul 2024, 04:58 It is currently 23 Jul 2024, 04:58
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Does the line with equation ax + by = c, where a, b and c are real con

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 22 Aug 2014
Posts: 14
Own Kudos [?]: 1039 [211]
Given Kudos: 7
Location: United States
Concentration: Human Resources, General Management
GPA: 3.97
WE:Information Technology (Insurance)
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11478
Own Kudos [?]: 34544 [115]
Given Kudos: 323
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6616 [67]
Given Kudos: 1646
Manager
Joined: 18 Jan 2010
Posts: 209
Own Kudos [?]: 1014 [62]
Given Kudos: 9
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
50
Kudos
12
Bookmarks
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.

(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. )
General Discussion
Manager
Joined: 12 Jan 2015
Posts: 154
Own Kudos [?]: 631 [2]
Given Kudos: 79
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
2
Kudos
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...?
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11478
Own Kudos [?]: 34544 [2]
Given Kudos: 323
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
1
Kudos
1
Bookmarks
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...?

Yes, Prakhar the line passing through ORIGIN crosses x-axis at x=0 and y-axis at y=0...
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6027
Own Kudos [?]: 13819 [7]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
6
Kudos
1
Bookmarks
Bunuel wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0

GMATinsight's Solution

A line will always cross x-axis if the slope of line is NOT zero

ax + by = c can be written as $$y = (-\frac{a}{b})x + (\frac{c}{b})$$

Comparing it with $$y = mx+c$$ where m is the slope

i.e. SLope of the given line $$= -\frac{a}{b}$$

Question REPHRASED: Is $$-\frac{a}{b}=0$$

Statement 1: b ≠ 0

but a may be 0 or non-zero hence

NOT SUFFICIENT

STatement 2: ab > 0

i.e. ab≠0

i.e. slope is non-zero i.e it will always cross x axis hence

SUFFICIENT

Senior Manager
Joined: 18 Feb 2020
Posts: 288
Own Kudos [?]: 175 [2]
Given Kudos: 30
Location: India
GMAT 1: 660 Q50 V29
GPA: 3
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
2
Kudos
Equation: ax+by=c
Rearranging, we get

y = (-a/b)x + (c/b)

Q: Does the line cross the x-axis? We need to find if the slope is 0 or not.

Statements:

(1) b ≠ 0

Doesn't tell anything about a. a can be 0 (line won't cross) or a can be something else (line will cross).

Insufficient.

(2) ab>0

Either a and b are both positive or both negative. Neither a nor b is equal to 0.

Therefore, we know that a is never zero. Does the line cross the x-axis? Definitely Yes.

Sufficient

Hence, the answer is Option (B).[/b]
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 8010
Own Kudos [?]: 4251 [1]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
1
Kudos
Bunuel wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0

Project DS Butler Data Sufficiency (DS3)

Eqn of line y =-ax/b+c/b
#1
B not = 0
Insufficient
#2
Ab>0

Possible when both are - or +

So eqn of line y=-x+c and y =-x-c

For values of x & y line will pass x axis slope is not 0
sufficient option B
Senior Manager
Joined: 22 Nov 2019
Posts: 260
Own Kudos [?]: 138 [0]
Given Kudos: 212
GPA: 4
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
Hi Bunuel,

I got stumped with this one on the mock. Can you help me clarify something.

For the line to not cross the x-axis, is it enough for the slope to be 0, or we also have to ensure that Y-Intercept is not equal to 0 (in other words if the line is the same as the X-Axis)?

I am guessing here, B was sufficient, as it is clear that slope is not 0, but if we knew the slope was 0, would the answer be E here, as we know nothing about the Y-Intercept?
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643203 [1]
Given Kudos: 86728
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
1
Kudos
TargetMBA007 wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0

Hi Bunuel,

I got stumped with this one on the mock. Can you help me clarify something.

For the line to not cross the x-axis, is it enough for the slope to be 0, or we also have to ensure that Y-Intercept is not equal to 0 (in other words if the line is the same as the X-Axis)?

I am guessing here, B was sufficient, as it is clear that slope is not 0, but if we knew the slope was 0, would the answer be E here, as we know nothing about the Y-Intercept?

The line represented by y = 0, while having a slope of 0, coincides with the x-axis. Whether coinciding lines can be considered as crossing each other is a technicality that the GMAT does not test. Fortunately, this specific case is ruled out by the second statement because ab > 0 implies that we don't have a y = 0 line.
Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
Moderator:
Math Expert
94580 posts