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

It is currently 22 Oct 2018, 00:50

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 278
In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 14 Mar 2012, 01:04
4
14
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (02:15) correct 58% (02:10) wrong based on 247 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Senior Manager
Senior Manager
avatar
B
Joined: 13 Mar 2012
Posts: 254
Concentration: Operations, Strategy
Re: DS co-ordinate geometry question  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 278
Re: DS co-ordinate geometry question  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
B
Joined: 13 Mar 2012
Posts: 254
Concentration: Operations, Strategy
Re: DS co-ordinate geometry question  [#permalink]

Show Tags

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

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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.


_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

Show Tags

New post 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
Manager
avatar
Joined: 03 May 2013
Posts: 69
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 01 Apr 2015
Posts: 53
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 03 May 2013
Posts: 69
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
Intern
avatar
B
Joined: 01 Jun 2016
Posts: 29
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
Intern
avatar
B
Joined: 01 Jun 2016
Posts: 29
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
IMG_20171105_235453.jpg [ 869.11 KiB | Viewed 780 times ]

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

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

Please refer to the attached graph.

Image
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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

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

Please refer to the attached graph.

Image
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 :dream: while solving this problem
Senior Manager
Senior Manager
avatar
P
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 50036
Re: In the xy-plane, if line k has negative slope, is the  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.