GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 08:08

### 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

# Line k is defined by the equation ax + by = c. If the slope of line k

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58428
Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

17 Jan 2019, 02:47
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

71% (01:04) correct 29% (01:11) wrong based on 86 sessions

### HideShow timer Statistics

Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?

A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

Updated on: 20 Jan 2019, 05:54
1
Bunuel wrote:
Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?

A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0

y=mx+c
given
ax+by=c
or say
ax-c=-by
y=- a/b x+c/b
-Y=a/bx-c/b
a/b <0
IMO B

Originally posted by Archit3110 on 17 Jan 2019, 07:16.
Last edited by Archit3110 on 20 Jan 2019, 05:54, edited 3 times in total.
Senior Manager
Joined: 13 Feb 2018
Posts: 450
GMAT 1: 640 Q48 V28
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

18 Jan 2019, 05:51
Got confused

Archit3110
Can you explain this part?

ax+by=c
or say
ax-c=by

Regards
L
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

18 Jan 2019, 06:05
1
LevanKhukhunashvili wrote:
Got confused

Archit3110
Can you explain this part?

ax+by=c
or say
ax-c=by

Regards
L

LevanKhukhunashvili

Solution attached

Posted from my mobile device
Attachments

File comment: Attached

IMG_20190118_183326967.jpg [ 3.49 MiB | Viewed 897 times ]

Intern
Joined: 12 Sep 2018
Posts: 27
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

20 Jan 2019, 01:28
1
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

Updated on: 20 Jan 2019, 05:53
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?

y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b<0...

Originally posted by Archit3110 on 20 Jan 2019, 01:44.
Last edited by Archit3110 on 20 Jan 2019, 05:53, edited 1 time in total.
Intern
Joined: 12 Sep 2018
Posts: 27
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

20 Jan 2019, 02:31
Archit3110 wrote:
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?

y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b>0...

But a/bx-c/b=-y is equal to y=-(a/b)x+c/b.
Therefore, as -(a/b) is the slope that has to positive, a/b has to be negative.
Attachments

File comment: a and b need to be one positive and one negative in order to make the slope of the line positive.

plot.jpg [ 361.6 KiB | Viewed 784 times ]

Manager
Joined: 28 May 2018
Posts: 144
Location: India
Schools: ISB '21 (II)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

20 Jan 2019, 04:38
artiom01 wrote:
Archit3110 wrote:
artiom01 wrote:
Archit3110

Shouldn't it be:

ax + by = c

by = -ax + c

y = -(a/b)x + c

?

y=mx+c
ax+by=c
ax-c=-by
question say : slope of line k is positive
a/bx-c/b=-y
so
a/b has to be +ve >0 ;
plot a graph you would get the relation on why a/b>0...

But a/bx-c/b=-y is equal to y=-(a/b)x+c/b.
Therefore, as -(a/b) is the slope that has to positive, a/b has to be negative.

I agree with artiom01. Can anyone point out where I am going wrong?
Bunuel
_________________
Please award KUDOS if my post helps. Thank you.
Intern
Joined: 10 Dec 2016
Posts: 21
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

20 Jan 2019, 04:49
Hi Bunuel,

Could you please explain how the ans is A instead of B.
Math Expert
Joined: 02 Sep 2009
Posts: 58428
Re: Line k is defined by the equation ax + by = c. If the slope of line k  [#permalink]

### Show Tags

20 Jan 2019, 05:49
Bunuel wrote:
Line k is defined by the equation ax + by = c. If the slope of line k is positive, which of the following must be true?

A. a/b > 0

B. a/b < 0

C. a > 0

D. b > 0

E. a + b > 0

$$ax + by = c$$;

$$y=-\frac{a}{b}*x+\frac{c}{b}$$;

The slope is -a/b. We are told that it's positive, so $$-\frac{a}{b}>0$$ --> $$\frac{a}{b}<0$$.

_________________
Re: Line k is defined by the equation ax + by = c. If the slope of line k   [#permalink] 20 Jan 2019, 05:49
Display posts from previous: Sort by