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

 It is currently 19 Jul 2018, 17:53

### 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
Your Progress

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

# In the xy-plane, if line k has negative slope, is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Jan 2010
Posts: 298
In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

14 Mar 2012, 01:04
4
13
00:00

Difficulty:

95% (hard)

Question Stats:

43% (01:43) correct 57% (01:39) wrong based on 243 sessions

### HideShow timer Statistics

In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

15 Mar 2012, 09:15
6
3
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line and $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$). So, basically we are asked whether $$b>0$$.

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of $$x$$ for $$y=0$$, so it's $$-\frac{b}{m}$$. The statement says that: $$-\frac{b}{m}<b$$ --> multiply by negative $$m$$ and flip the sign of the inequality: $$-b>bm$$ --> $$b(m+1)<0$$. Now, in order $$b>0$$ to be true $$m+1$$ should be negative, so the question becomes: is $$m+1<0$$? --> is $$m<-1$$. We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is $$m<-1$$?" and (2) says that $$m<-2$$. Sufficient.

Answer: C.
_________________
##### General Discussion
Senior Manager
Joined: 13 Mar 2012
Posts: 294
Concentration: Operations, Strategy
Re: DS co-ordinate geometry question  [#permalink]

### Show Tags

14 Mar 2012, 01:51
2
1
vdadwal wrote:
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?

let me try:
we have line k say: y=mx+c
we need to find if c>0

1) x-intercept, i.e. y=0
x=-c/m
y-intercept, i.e. x=0
y=c

hence -c/m<c
=> c*((1/m)+1)>0

i.e. for different value of "m", "c" can be both positive and negative

hence insufficient

2) cant infer anything about c
insufficient

1+2

if m<-2

c*(m+1)<0 (m<0 hence sign change)
as m<-2
hence m+1<-1
i.e. negative
i.e. c>0

Sufficient

hence C

hope it helps..!!!
_________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS
If there's a loophole in my analysis--> suggest measures to make it airtight.

Senior Manager
Joined: 21 Jan 2010
Posts: 298
Re: DS co-ordinate geometry question  [#permalink]

### Show Tags

14 Mar 2012, 02:07
thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,

Explanation

If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the x-intercept, we can answer the question.

Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the x-intercept is -4, the y-intercept could be -2. This is a relatively flat slope--as it turns out, it's true if the slope is greater than -1. It's also possible that both intercepts are positive. For instance, if the x-intercept is 3, the y-intercept could be 5. The negative slope here is steeper--in general, less than -1.

Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative intercepts--the slope of the line doesn't determine the location of the line.

Taken together, the statements are sufficient. In (1), we learned that if the slope is less than -1, both intercepts are positive. Since the slope is less than -2, both intercepts must be positive. Choice (C) is correct.

Can you help ?

thanks
Senior Manager
Joined: 13 Mar 2012
Posts: 294
Concentration: Operations, Strategy
Re: DS co-ordinate geometry question  [#permalink]

### Show Tags

14 Mar 2012, 20:11
vdadwal wrote:
thanks , i also got the following explanation and dont understand the logic behind their deduction from 1 ,

Explanation

If a line has negative slope, the intercepts will have the same sign. So if we can find the sign of the x-intercept, we can answer the question.

Statement (1) is insufficient. It's possible that both intercepts are negative, for instance if the x-intercept is -4, the y-intercept could be -2. This is a relatively flat slope--as it turns out, it's true if the slope is greater than -1. It's also possible that both intercepts are positive. For instance, if the x-intercept is 3, the y-intercept could be 5. The negative slope here is steeper--in general, less than -1.

Statement (2) is also insufficient. Such a slope is relatively steep, but it could result in positive or negative intercepts--the slope of the line doesn't determine the location of the line.

Taken together, the statements are sufficient. In (1), we learned that if the slope is less than -1, both intercepts are positive. Since the slope is less than -2, both intercepts must be positive. Choice (C) is correct.

Can you help ?

thanks

proceed graphically and check the slope,
1) when the intercepts are in first quadrant, you will see the slope should be less than tan(135)
i.e. less than -1 to satisfy the condition y>x intercept. (at -1 you will see x=y intercept)
similarly, when in third quadrant slope should be greater than tan (135) i.e. -1

insufficient

2) insufficient

both 1 and 2 slope less than -2 i.e. less than -1 hence both intercept are positive.

hope this clarifies
_________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS
If there's a loophole in my analysis--> suggest measures to make it airtight.

Intern
Joined: 31 Jul 2014
Posts: 20
In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

11 Aug 2014, 05:13
Bunuel,

I dont understand

-b/m<b --> multiply by negative m and flip the sign of the inequality: -b>bm --> b(m+1)<0... can you explain?

IF -b/m<b, then -b<bm....b(m+1)>0...Can you explain how b(1+m) < 0?
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

12 Aug 2014, 08:30
saikrishna123 wrote:
Bunuel,

I dont understand

-b/m<b --> multiply by negative m and flip the sign of the inequality: -b>bm --> b(m+1)<0... can you explain?

IF -b/m<b, then -b<bm....b(m+1)>0...Can you explain how b(1+m) < 0?

When you multiply by a negative value you must flip the sign of the inequality.

_________________
Intern
Joined: 31 Jul 2014
Posts: 20
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

13 Aug 2014, 07:49
-b/m<b --> If we multiply by negative m, we have to flip the sign as well as multiply by -m on both sides. Isnt this correct?

If I multiply (left side equation) -b/m by -m => -b/m*-m => b
If I multiply (right side equation) b by -m => -b*m
If I flip the sign,

(Left side) b > -b*m (right side) => b(1+m) > 0....Where did I go wrong? Please clarify my concept.
Manager
Joined: 03 May 2013
Posts: 72
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

01 Nov 2015, 03:02
hi bunuel plz explain, why the sing of m is not considered here( at x intersept) y = mx +b , x = -b/m, why its not x = b/m(taking -m, negative slope)
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

01 Nov 2015, 09:07
vipulgoel wrote:
hi bunuel plz explain, why the sing of m is not considered here( at x intersept) y = mx +b , x = -b/m, why its not x = b/m(taking -m, negative slope)

You do not substitute a variable, say x, by -x if you know that x is negative. This does not make sense.
_________________
Manager
Joined: 01 Apr 2015
Posts: 57
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

04 Nov 2015, 08:19
Hi Bunuel,

I have the same doubt as vipulgoel, however i couldn't understand your follow-up explanation. Since we know m is negative, shouldnt we take the sign into consideration ? Could you please explain what do you mean by "you do not substitute a variable say, x by -x" ?

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

04 Nov 2015, 09:50
1
Swaroopdev wrote:
Hi Bunuel,

I have the same doubt as vipulgoel, however i couldn't understand your follow-up explanation. Since we know m is negative, shouldnt we take the sign into consideration ? Could you please explain what do you mean by "you do not substitute a variable say, x by -x" ?

Thanks.

Say it's given that x=a, and you know that x is negative do you substitute x by -x in this case? No.
_________________
Manager
Joined: 03 May 2013
Posts: 72
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

06 Nov 2015, 22:08
hi, Let me try , y = mx+ c is a general form, irrespective of slope, first just write x intercept (without considering - ve slope), now as Bunuel did multiply with -m(negative slope on both sides, that's how -ve slope comes in picture)
Intern
Joined: 01 Jun 2016
Posts: 29
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

06 Sep 2017, 20:47
Bluelagoon wrote:
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?

Before we start let's revise a rule, which says that if a line has -ve slope, then either both the intercept will be -ve or both will be +ve. They cannot have different sign.

or

the line can pass from (0,0) i.e origin we are not considering this case.

Answer: C

Let's say X intercept is A and Y intercept is B

1)

says A < B ...(I)
now as the slope is -ve. A and B both can be -ve or +ve.
Insufficient.

2)

slope is -2.
Formula of slope is \frac{Y-intercept}{X-Intercept}
so, \frac{B}{A} = -2 ...(II)
again, A and B both can be -ve or +ve.
Insufficient

Together

from II, \frac{B}{-2} = A
substitute the above value in I,
\frac{B}{-2} < B
Multiply the above fraction by -2,
B > -2B
3B > 0, hence B is greater than 0.
sufficient
Intern
Joined: 01 Jun 2016
Posts: 29
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

06 Sep 2017, 20:48
Bluelagoon wrote:
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

(1) The x-intercept of line k is less than the y-intercept of line k.

(2) The slope of line k is less than -2.

It is a DS question, can you help and explain the answer?

Before we start let's revise a rule, which says that if a line has -ve slope, then either both the intercept will be -ve or both will be +ve. They cannot have different sign.

or

the line can pass from (0,0) i.e origin we are not considering this case.

Answer: C

Let's say X intercept is A and Y intercept is B

1)

says A < B ...(I)
now as the slope is -ve. A and B both can be -ve or +ve.
Insufficient.

2)

slope is -2.
Formula of slope is \frac{Y-intercept}{X-Intercept}
so, \frac{B}{A} = -2 ...(II)
again, A and B both can be -ve or +ve.
Insufficient

Together

from II, \frac{B}{-2} = A
substitute the above value in I,
\frac{B}{-2} < B
Multiply the above fraction by -2,
B > -2B
3B > 0, hence B is greater than 0.
sufficient
Senior Manager
Joined: 02 Apr 2014
Posts: 486
GMAT 1: 700 Q50 V34
In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

05 Nov 2017, 11:29
Hi Bunuel

Please refer to the attached graph.

Line 1:
has slope < -2 and x intercept = -1.5 which is less than y-intercept = -1 => y-intercept is -ve

Line 2:
has slope < -2 and x intercept = 1 which is less than y-intercept = 1.5 => y-intercept is +ve

So the answer must E ..right?

Or am i missing anything?
Attachments

IMG_20171105_235453.jpg [ 869.11 KiB | Viewed 708 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

05 Nov 2017, 11:39
hellosanthosh2k2 wrote:
Hi Bunuel

Please refer to the attached graph.

Line 1:
has slope < -2 and x intercept = -1.5 which is less than y-intercept = -1 => y-intercept is -ve

Line 2:
has slope < -2 and x intercept = 1 which is less than y-intercept = 1.5 => y-intercept is +ve

So the answer must E ..right?

Or am i missing anything?

The correct answer is C, as explained here: https://gmatclub.com/forum/in-the-xy-pl ... l#p1058889

The slope of a line passing through (1, 0) and (0, 1.5) is -1.5, which is not less than -2, as per (2).
The slope of a line passing through (-1.5, 0) and (0, -1) is -0.67, which is not less than -2, as per (2).
_________________
Senior Manager
Joined: 02 Apr 2014
Posts: 486
GMAT 1: 700 Q50 V34
In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

05 Nov 2017, 12:02
Bunuel wrote:
hellosanthosh2k2 wrote:
Hi Bunuel

Please refer to the attached graph.

Line 1:
has slope < -2 and x intercept = -1.5 which is less than y-intercept = -1 => y-intercept is -ve

Line 2:
has slope < -2 and x intercept = 1 which is less than y-intercept = 1.5 => y-intercept is +ve

So the answer must E ..right?

Or am i missing anything?

The correct answer is C, as explained here: https://gmatclub.com/forum/in-the-xy-pl ... l#p1058889

The slope of a line passing through (1, 0) and (0, 1.5) is -1.5, which is not less than -2, as per (2).
The slope of a line passing through (-1.5, 0) and (0, -1) is -0.67, which is not less than -2, as per (2).

Thanks Bunuel , i realized my mistake slope of Line 1 (-1/1.5) is not less than (-2), Line 1 is not possible.

I must have been half asleep while solving this problem
Senior Manager
Joined: 31 Jul 2017
Posts: 374
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

06 Nov 2017, 02:25
Bunuel wrote:
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line and $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$). So, basically we are asked whether $$b>0$$.

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of $$x$$ for $$y=0$$, so it's $$-\frac{b}{m}$$. The statement says that: $$-\frac{b}{m}<b$$ --> multiply by negative $$m$$ and flip the sign of the inequality: $$-b>bm$$ --> $$b(m+1)<0$$. Now, in order $$b>0$$ to be true $$m+1$$ should be negative, so the question becomes: is $$m+1<0$$? --> is $$m<-1$$. We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is $$m<-1$$?" and (2) says that $$m<-2$$. Sufficient.

Answer: C.

Hi Bunuel,

I have doubt here.. can you please help me to understand it
if -b/m<b, then can we write m>-1?? by cancelling b on both sides.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

### Show Tags

06 Nov 2017, 02:27
rahul16singh28 wrote:
Bunuel wrote:
In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line and $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$). So, basically we are asked whether $$b>0$$.

(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of $$x$$ for $$y=0$$, so it's $$-\frac{b}{m}$$. The statement says that: $$-\frac{b}{m}<b$$ --> multiply by negative $$m$$ and flip the sign of the inequality: $$-b>bm$$ --> $$b(m+1)<0$$. Now, in order $$b>0$$ to be true $$m+1$$ should be negative, so the question becomes: is $$m+1<0$$? --> is $$m<-1$$. We don't know that. Not sufficient.

(2) The slope of line k is less than -2. Insufficient on its own.

(1)+(2) From (1) the question became: "is $$m<-1$$?" and (2) says that $$m<-2$$. Sufficient.

Answer: C.

Hi Bunuel,

I have doubt here.. can you please help me to understand it
if -b/m<b, then can we write m>-1?? by cancelling b on both sides.

No. You cannot reduce an inequality by a variable unless you know its sign. If the variable is positive you should keep the sign but if the variable is negative you should flip the sign of the inequality.
_________________
Re: In the xy-plane, if line k has negative slope, is the &nbs [#permalink] 06 Nov 2017, 02:27

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

# In the xy-plane, if line k has negative slope, is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.