Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

algebric exxpression

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 96
Joined: Fri Apr 23, 2010 1:14 amFollowed by: 1 member
Thanked: 1 times
by quantskillsgmat » Wed Jan 04, 2012 12:11 am
If x and y both are positive and x+y=1.what is minimum value of (x+1/x)^2+ (y+1/y)^2
a)12
b)20
c)12.5
d)13.3
Top
Join the discussion
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 96
Joined: Fri Apr 23, 2010 1:14 amFollowed by: 1 member
Thanked: 1 times

by quantskillsgmat » Wed Jan 04, 2012 12:13 am
a,b,c and d are 4 positive real numbers.and their product is 1.what is minimum value of (1+a)(1+b)(1+c)(1+d)
a)4
b)1
c)16
d)18
Top
Join the discussion
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Wed Jan 04, 2012 8:35 am
I really don't know if theres a proper method to do these problems you post. Most of them don't seem to be GMAT problems. Pls refrain posting random problems which are not within the scope of the exam.

I assume x=y=1/2 -> x+y =1

(5/2)^2 + (5/2)^2 = 12.5
quantskillsgmat wrote:If x and y both are positive and x+y=1.what is minimum value of (x+1/x)^2+ (y+1/y)^2
a)12
b)20
c)12.5
d)13.3
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 385
Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members
Thanked: 62 times

by user123321 » Wed Jan 04, 2012 8:56 am
quantskillsgmat wrote:a,b,c and d are 4 positive real numbers.and their product is 1.what is minimum value of (1+a)(1+b)(1+c)(1+d)
a)4
b)1
c)16
d)18
since all are +ve. lets assume a=b=c=d=1, then you will get 16.
any other values apart from above like 1,1,2,1/2 will actually be above 16.
so min should be 16.

user123321
Just started my preparation :D
Want to do it right the first time.
Top
Join the discussion
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Wed Jan 04, 2012 10:06 am
either 1/x or 1/y is close to 1
if 1/x is close to 1, then x is close to 1 and y is close to 0. One of fractions gets maximized, therefore take x=1/2 and y=1/2
(1/2+2)^2+(1/2+2)^2=50/4=12.5
c
quantskillsgmat wrote:If x and y both are positive and x+y=1.what is minimum value of (x+1/x)^2+ (y+1/y)^2
a)12
b)20
c)12.5
d)13.3
Success doesn't come overnight!
Top
Join the discussion
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Wed Jan 04, 2012 10:26 am
abcd must be four numbers, either whole or fractional. If whole their values is 1 and a=b=c=d
If fractional these numbers must cancel each other, e.g. 1/2*2*1/3*3.
In any case all fractional numbers added by one will be greater than a=b=c=d=1
hence, we minimize by 2^4=16
c

quantskillsgmat wrote:a,b,c and d are 4 positive real numbers.and their product is 1.what is minimum value of (1+a)(1+b)(1+c)(1+d)
a)4
b)1
c)16
d)18
Success doesn't come overnight!
Top
Join the discussion