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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

1) + 2) Z^2 > (1-Z)^2 => Z must be greater than 0.5, graph it to see it clearly, either as a line or two intersecting parabolas facing up. so Z>0.5 and Y<0.5 sufficient

sparky, Just curious, how did you hone in on 0.5

i think, to hold the both equation, Z must be more than 0.5. i also agree with him/her.

i think, to hold the both equation, Z must be more than 0.5. i also agree with him/her.

Any calculations?

WinWinMBA wrote:

Is Y < Z ? 1. Y + Z = 1 2. Y^2 < Z^2

we know, from i, y and z could be anything, but their sum must be 1.
from ii, y and z could be both +ve and -ve.

from i and ii, z cannot be smaller than y because if z is smaller than y, the equation in i and ii do not hold.

so lets plug innnnnnnnnnnnnn......

if z = 1, y = 0=> possible
if z = 10, y = -9=>possible
if z = 0, y = 1 = > not possible because the eq z^2>y^2 doesnot satisy. so any value for z less than the y"s value doesnot satisfy the eqs.

so now lets plug in for some other values that are lowest for z:
if z = 0.9, y = .1, both equations are satisfied.
if z = 0.6, y = .4, both equations are satisfied.
if z = 0.51, y = .49, both equations are satisfied.
if z = 0.5, y = .5, both equations are not satisfied. so we cannot go for any value for z that is not more than 0.5 because sq of z must greater than the sq of y.

HIMALAYA, Thanks for your time. Your thought process is similar to mine. plugging innnnnnnnnnnn. But I was curious to know of a less time consuming approach.

Sparky's approach looks a lot quicker than our plugging innnnnnnn.

HIMALAYA, Thanks for your time. Your thought process is similar to mine. plugging innnnnnnnnnnn. But I was curious to know of a less time consuming approach.

Sparky's approach looks a lot quicker than our plugging innnnnnnn.

yes, sparky's approach is indeed a lot faster. Nice one

I just want to say something. When dealing with inequialities, try to solve them.

If you are plugging numbers on inequalities questions, you are pretty much doomed, unless you know what numbers to plug. But to know what numbers to plug, you need to have a general notion/sense how that particular inequality works which you might not have unless you have a lot of experince or are in a genious category.

Since it's all about signs try to get them in the following form

()*()/()*() >< 0

I bet you the things in brackets will correspond closely to what is given in 1) and 2)

HIMALAYA, Thanks for your time. Your thought process is similar to mine. plugging innnnnnnnnnnn. But I was curious to know of a less time consuming approach.

Sparky's approach looks a lot quicker than our plugging innnnnnnn.

yes, sparky's approach is indeed a lot faster. Nice one

ohhh yes, i agree with you guys. just trying to show how values of y and z are <0.5 and more than 0.5 respectively.........

we can do in many ways, but, of course, we need a shortest one. this could be one of them:

from i, z=1-y ..............................1
from ii, y^2<z^2 .........................2

lets put the value of z in 1 to eq 2: y^2 <(1-y)^2
solving the eq ....... y^2 < 1-2y+y^2
2y<1
so y<1/2. if y<1/2 or 0.5, then z >1/2 0r 0.5.