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 →

r = ½ (3 p + q) and s = p – q

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760
by sanju09 » Thu Sep 16, 2010 11:29 pm
If r = ½ (3 p + q) and s = p - q, for which of the following values of p would r^2 = s^2?
(A) q/5
(B) 10 - 1½ q
(C) q - 1
(D) 3 q
(E) 4½ q - 9



[spoiler]Source: https://www.west.net/~stewart/gmat[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

by goyalsau » Thu Sep 16, 2010 11:44 pm
Is it A,
If its A then i would like to see the short cut because i did is really lengthy.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Fri Sep 17, 2010 12:08 am
goyalsau wrote:Is it A,
If its A then i would like to see the short cut because i did is really lengthy.
[spoiler]yes[/spoiler]


If r^2 = s^2, then:

[½ (3 p + q)] ^2 = [p - q] ^2

Work it out, segregate zero on one side of the equation, then factor the quadratic expression into two binomials. Find the two roots of p by setting each binomial equal to 0; [spoiler]q/5[/spoiler] will be one of the two.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 74
Joined: Sun Sep 05, 2010 3:11 pm
Thanked: 3 times

by klmehta03 » Sun Sep 19, 2010 4:48 pm
yup the ans is A..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 17
Joined: Tue Aug 24, 2010 4:51 am
Location: Sydney, Australia
Thanked: 1 times

by kaushiksin » Mon Sep 20, 2010 3:28 am
r = ½ (3 p + q) and s = p - q

Lets start with choice A

P = q/5
r = 1/2 (3q/5+q) = 1/2 (8q/5) = 4q/5

s = q/5-q = -4q/5

r^2 = s^2
16q^2/25 = 16q^2/25

Hence, the answer is (A)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1