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:

From (2) X and Y could be either positive or negative, thus, (2) alone is also not sufficient.

Combine => X&Y are positive.

Looks like the answer is E.

IMO, I think you need to re=examine your analysis for condition (1). _________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

Re: Is x>y? (1) square root x>square root y (2) x^2>y^2 [#permalink]

Show Tags

15 Jan 2012, 04:08

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

Konstantin Lynov wrote:

An old one:

Is X>Y ?

(1) square root X > square root Y (2) X^2 > Y^2

Through the discussion people agreed that the answer is A, since on the GMAT we are dealing only with arithmetic radicals and, therefore, sqrt(X) and sqrt(Y) are non negative.

Disagree on that answer is:

USEFUL TO KNOW A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality). For example: \(2<4\) --> we can square both sides and write: \(2^2<4^2\); \(0\leq{x}<{y}\) --> we can square both sides and write: \(x^2<y^2\);

But if either of side is negative then raising to even power doesn't always work. For example: \(1>-2\) if we square we'll get \(1>4\) which is not right. So if given that \(x>y\) then we can not square both sides and write \(x^2>y^2\) if we are not certain that both \(x\) and \(y\) are non-negative.

B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality). For example: \(-2<-1\) --> we can raise both sides to third power and write: \(-2^3=-8<-1=-1^3\) or \(-5<1\) --> \(-5^2=-125<1=1^3\); \(x<y\) --> we can raise both sides to third power and write: \(x^3<y^3\).

Is x>y?

(1) \(\sqrt{x}>\sqrt{y}\) --> as both parts of the inequality are non-negative then according to A we can square them --> \(x>y\). Sufficient.

(2) \(x^2>y^2\) --> \(|x|>|y|\) --> \(x\) is farther from zero than \(y\), but this info is insufficient to say whether \(x>y\) (if \(x=2\) and \(y=1\) - YES but \(x=-2\) and \(y=1\) - NO). Not sufficient.

1, square root X > square root Y Consider value: x=9, y= 4 so, suare root of 9 = 3, AND 4 = 2, AND 9>4 so AD... 2, X^2>Y^2 here x= 1,y= 2 so 1 is not greater than 2, so

1, square root X > square root Y Consider value: x=9, y= 4 so, suare root of 9 = 3, AND 4 = 2, AND 9>4 so AD... 2, X^2>Y^2 here x= 1,y= 2 so 1 is not greater than 2, so

only A....

can we consider negative values in square root??

You cannot get sufficiency based only on one set of numbers. Thus theoretically testing only one set of numbers can give you an incorrect answer.

As for your other questions: the even roots from negative numbers are not defined for the GMAT, which means that for \(\sqrt{x}\) to be defined, x must be more than or equal to zero.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

1, square root X > square root Y Consider value: x=9, y= 4 so, suare root of 9 = 3, AND 4 = 2, AND 9>4 so AD... 2, X^2>Y^2 here x= 1,y= 2 so 1 is not greater than 2, so

only A....

can we consider negative values in square root??

You cannot get sufficiency based only on one set of numbers. Thus theoretically testing only one set of numbers can give you an incorrect answer.

As for your other questions: the even roots from negative numbers are not defined for the GMAT, which means that for \(\sqrt{x}\) to be defined, x must be more than or equal to zero.

Hope it's clear.

But what about taking negative root of a number?

So in this case, what if we take negative root of X and positive root of Y? In that case option A won't be sufficient...

1, square root X > square root Y Consider value: x=9, y= 4 so, suare root of 9 = 3, AND 4 = 2, AND 9>4 so AD... 2, X^2>Y^2 here x= 1,y= 2 so 1 is not greater than 2, so

only A....

can we consider negative values in square root??

You cannot get sufficiency based only on one set of numbers. Thus theoretically testing only one set of numbers can give you an incorrect answer.

As for your other questions: the even roots from negative numbers are not defined for the GMAT, which means that for \(\sqrt{x}\) to be defined, x must be more than or equal to zero.

Hope it's clear.

But what about taking negative root of a number?

So in this case, what if we take negative root of X and positive root of Y? In that case option A won't be sufficient...

Where am I going wrong?

Thanks in advance! NB

I am assuming that you are talking about taking the negative square of a number? Something similar to , if given x^2 > y^2 ---> \(\sqrt{x^2} > \sqrt{y^2}\) ?

Note that for GMAT, square root of any positive number 'x' = \(\sqrt {x}\) \(\geq\) 0. There are no 'negative' square roots for GMAT.

• \(\sqrt{x^2}=|x|\), when x≤0, then \(\sqrt{x^2}=−x\) and when x≥0, then \(\sqrt{x^2}=x\)

• When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

So in this case, what if we take negative root of X and positive root of Y? In that case option A won't be sufficient...

Where am I going wrong?

Thanks in advance! NB[/quote]

I am assuming that you are talking about taking the negative square of a number? Something similar to , if given x^2 > y^2 ---> \(\sqrt{x^2} > \sqrt{y^2}\) ?

Note that for GMAT, square root of any positive number 'x' = \(\sqrt {x}\) \(\geq\) 0. There are no 'negative' square roots for GMAT.

• \(\sqrt{x^2}=|x|\), when x≤0, then \(\sqrt{x^2}=−x\) and when x≥0, then \(\sqrt{x^2}=x\)

• When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I may have spoken to over 50+ Said applicants over the course of my year, through various channels. I’ve been assigned as mentor to two incoming students. A...