BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

slope

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 876
Joined: Thu Apr 10, 2008 8:14 am
Thanked: 13 times
by ketkoag » Tue Jun 09, 2009 7:13 am
Line L pass point (a, b) and (c,d), if slope <0
1) (a-c)*(b-d)<0
2) Product of interceptions on axis-x and axis-y >0

Here, please tell me how second statement is suff. Also by first statement I took some values and checked, the slope is coming to be positive. will it always be true?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sat May 30, 2009 2:49 am
Thanked: 9 times

by SanjeevK » Tue Jun 09, 2009 9:02 am
[spoiler]IMO D:[/spoiler]

Since L passes through (a,b) and (c,d), the slope of line is (d-b)/(c-a) or (b-d)/(a-c)

A: (a-c)*(b-d)<0. This means either (a-c) or (b-d) has to be negative but not both. Hence slope will be negative. Sufficient
B: The equation of the line will be y = [(b-d)/(a-c)] x + k (where k is a constant)
The y intercept will be (0,k) and x intercept will be -k(a-c)/(b-d)
Product of x intercept and y intercept is positive.
=> [-k(a-c)/(b-d)]k >0
=> -(k^2)(a-c)/(b-d) > 0. This means (a-c)/(b-d) < 0 . This means slope is negative. Sufficient

Hope this helps
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 170
Joined: Tue May 26, 2009 12:00 pm
Thanked: 5 times

by yogami » Tue Jun 09, 2009 11:07 am
SLope is always (y1 - y2)/(x1 - x2) which is (d - b)/(c - a). We want to prove if this ratio is < 0
(1) says the product is negative. If two numbers when multiplied are negative they will be negative when divided too, so slope is also negative hence sufficient
(2) if products of x and y intercepts are positive this implies those intercepts are both positive or both negative. Now visualize the line. LIne is cutting the x and y axis at positive x and positive y axis somewhere bending towards left like this \. And any line like that has -ve slope. That line can also be cutting -ve x axis and -ve y axis too and still have its shape \. hence sufficient

so D
200 or 800. It don't matter no more.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1