Lines n and p lie in the xy-plane. Is the slope of line n

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 20 Feb 2012

Posts: 45

Followers: 0

Kudos [?]: 17 [0], given: 6

Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

23 Feb 2012, 08:07

00:00

Question Stats:

60% (01:47) correct

39% (00:51) wrong

based on 12 sessions

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

[Reveal] Spoiler: OA

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11600

Followers: 1800

Kudos [?]: 9592 [7] , given: 828

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

23 Feb 2012, 08:11

This post received
KUDOS

BANON wrote:

Algebraic approach:

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

We have two lines: y_n=m_1x+b_1 and y_p=m_2x+b_2. Q: m_1<m_2 true?

(1) Lines n and p intersect at the point (5,1) --> 1=5m_1+b_1=5m_2+b_2 --> 5(m_1-m_2)=b_2-b_1. Not sufficient.
(2) The y-intercept of line n is greater than the y-intercept of line p --> y-intercept is value of y for x=0, so it's the value of b --> b_1>b_2 or b_2-b_1<0. Not sufficient.

(1)+(2) 5(m_1-m_2)=b_2-b_1, as from (2) b_2-b_1<0 (RHS), then LHS (left hand side) also is less than zero 5(m_1-m_2)<0 --> m_1-m_2<0 --> m_1<m_2. Sufficient.

Answer: C.

For more on this topic check Coordinate Geometry Chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11600

Followers: 1800

Kudos [?]: 9592 [0], given: 828

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

23 Feb 2012, 08:13

BANON wrote:

Graphic approach:

Lines n and p lie in the xy plane. Is the slope of line n less than the slope of line p?

(1) Lines n and p intersect at (5,1)
(2) The y-intercept of line n is greater than y-intercept of line p

The two statements individually are not sufficient.

(1)+(2) Note that a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

Attachment:

1.PNG [ 14.29 KiB | Viewed 2785 times ]

If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the absolute value of its slope is greater than the absolute value of the slope of the line p, so the slope of n is more negative than the slope of p, which means that the slope of p is greater than the slope of n:

Attachment:

2.PNG [ 13.66 KiB | Viewed 2783 times ]

So in both cases the slope of p is greater than the slope of n. Sufficient.

Answer: C.
_________________

Intern

Joined: 04 Jan 2012

Posts: 8

GPA: 3.97

WE: Analyst (Mutual Funds and Brokerage)

Followers: 0

Kudos [?]: 0 [0], given: 12

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

23 Feb 2012, 09:05

Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11600

Followers: 1800

Kudos [?]: 9592 [0], given: 828

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

23 Feb 2012, 10:13

nglekel wrote:

Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

If line p has a negative y-intercept then its slope is positive and it will still be more than the slope of n, with positive y-intercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive y-intercept and you'll easily see the answer.

Check the following links for similar questions, where different scenarios are considered:
in-the-xy-plane-is-the-slope-of-line-l-greater-than-the-126941.html
if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html
slopes-of-m-and-n-124025.html

Also check Coordinate Geometry chapter of Math Book for theory on this subject: math-coordinate-geometry-87652.html

Hope it helps.
_________________

Manager

Joined: 05 Jul 2012

Posts: 83

Location: India

Concentration: Finance, Strategy

GMAT Date: 09-30-2012

GPA: 3.08

WE: Engineering (Energy and Utilities)

Followers: 4

Kudos [?]: 6 [0], given: 8

Re: Lines n and p lie in the xy-plane. Is the slope of line n le [#permalink]

13 Sep 2012, 12:19

monikaleoster wrote:

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?
(1) Lines n and p intersect at the point (5,1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

Here we have two lines and two slopes
So lets first write the equations for our lovely lines

Y = mnX + Cn
Y = mpX + Cp

Now statement one says that it intersects at 5,1. SO lets put it in the equations and subtract them

We get, (mn-mp)5 = Cp-Cn that tells us nothing about the slopes of the lines or their relative values, but if we know the value of Cp-Cn that weather it is positive or negative we will know weathet mn-mp is positive or negative and that which is greater

Statement 2 Y intercept of line n is greater than p so that gives us Cn >Cp

Alone this statement is also not sufficient. it talks abou c not slopes

But if we combine the two, Voila !! we know which slope is greater.

Intern

Joined: 31 Oct 2011

Posts: 19

Schools: ESSEC '15 (A)

GMAT 1: 650 Q45 V35

Followers: 0

Kudos [?]: 3 [0], given: 2

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

29 Dec 2012, 09:18

I don't get it :/

what if slope of line P is positive and the slope of line N negative (but still satisfying all the condition...)
Bunuel, on your examples the slopes have the same sign... are we talking about the absolute value of the slope?

Manager

Joined: 02 Sep 2012

Posts: 211

Location: United States

Concentration: Entrepreneurship, Finance

GMAT Date: 07-25-2013

GPA: 3.83

WE: Architecture (Computer Hardware)

Followers: 1

Kudos [?]: 29 [0], given: 66

Lines n and p lie in the xy plane. Is the slope of the line [#permalink]

29 Apr 2013, 08:39

Lines n and p lie in the xy plane. Is the slope of the line n less than the slope of line p?

(1) Lines n and p intersect at the point (5,1)
(2) The X-intercept of line n is greater than the X-intercept of line p
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11600

Followers: 1800

Kudos [?]: 9592 [0], given: 828

Re: Lines n and p lie in the xy plane. Is the slope of the line [#permalink]

29 Apr 2013, 08:44

skamal7 wrote:

Merging similar topics. Please ask if anything remains unclear.
_________________

Manager

Joined: 02 Sep 2012

Posts: 211

Location: United States

Concentration: Entrepreneurship, Finance

GMAT Date: 07-25-2013

GPA: 3.83

WE: Architecture (Computer Hardware)

Followers: 1

Kudos [?]: 29 [0], given: 66

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

29 Apr 2013, 09:07

The question which is posted differs with the statement 2...Pls do have a look at it..will the answers remain the same?
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink] 29 Apr 2013, 09:07

		Similar topics	Author	Replies	Last post
Similar Topics:		Line n and p lie in the xy plane. Is the slope of line n	Jennif102	4	09 Dec 2005, 21:15
		Lines n and p lie in the xy-plane. Is the slope of line n	dinesh8	17	07 May 2006, 18:24
		lines n and p lie in the xy-plane. is the slope of line n	lan583	4	24 Aug 2006, 15:31
		Lines n and p lie in the xy-plane. Is the slope of line n	alimad	2	25 Sep 2006, 22:37
	1	Lines n and p lie in the xy-plane. Is the slope of line n	artshep	9	11 Nov 2006, 13:28

Lines n and p lie in the xy-plane. Is the slope of line n

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

Lines n and p lie in the xy-plane. Is the slope of line n

Lines n and p lie in the xy-plane. Is the slope of line n

Main navigation

GMAT Resources

Partners

MBA Resources