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:

I do not agree OA and OE. Please provide explanation

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake. _________________

If You're Not Living On The Edge, You're Taking Up Too Much Space

I do not agree OA and OE. Please provide explanation

Attachment:

math.JPG

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake.

GMAT considers only +ve value for Sqrt()

Sqrt(x) --> lead only one +ve solution.

X^2=4 then both +ve and -ve are valid solutions. _________________

Your attitude determines your altitude Smiling wins more friends than frowning

I do not agree OA and OE. Please provide explanation

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake.

Reply:

If you graph the square root of a number then the graph will always be on the positive side. This is a basic principle of math that we learned from pre-calculus course or even earlier. Even Calculus text-book should have them. This is how i see why square root is always positive.

Another way to see this, rt ( -4) doesn't exist because you can not square a number and then get a negative number. I believe that GMAT doesn't want you to break it down from rt(4) to +2/-2. They want you to take it as is. If its rt(4) then you should take it as x=4

You can see the OA by clicking "Reveal" in the spoiler under the question.

RenukaD wrote:

What is the OA?

Thanks dzyubam . my answer was also A but ,looking at posts above, which says "GMAT does not consider -ve values of root" so by this are we trying to say in this case "C" is sufficient condition ? If not then in what scenario we should consider only positive values of roots.

Thanks in advance _________________

_________________ If you like my post, consider giving me a kudos. THANKS!

1) X^(1/2) > Y^(1/2) - Because X and Y are under a square-root they can only be positive, or imaginery numbers. thus we can conclude that statment 1 is sufficient.

2) X^2 > Y^2 - This statement tells us that the absolute value of X is greater than Y, but we cannot determine that X is greater than Y, thus this statement is insufficient. For instance: X=3, -3 Y=2, -2

(I) if \sqrt{x}>\sqrt{y} x>y...\sqrt{x} can only be \(>=\) 0 x,y are > 0....hence x > y Sufficient

(II) if x^2 > y^2 x^2 - y^2 >0 (x+y) or (x-y) > 0 both brackets need to be positive or negative.

Both brackets positive: x=4, y= -2; (4-2)(4--2)>0 from here, we have (4-2)(4+2)>0 And x(4) > y.....response is YES sufficient

Both brackets Negative: x=-4; y= -2 (-4 -2) and (-4 +2) from here, we have: (-4-2)(-4+2)>0 And x(-4) < y(-2).....response is NO insufficient So, II is INSUFFICIENT

OA is A. SImply put, test the pair of numbers with different signs: (i) x(4) and y(2) (ii) x(-4) and y(-2) ... and you will realize the insufficiency in II. _________________

KUDOS me if you feel my contribution has helped you.

Please elaborate on that. You mean GMAT considers all radical terms positive?

For example, \(\sqrt{4}\) can only be 2, whereas \(x^2=4\) x can be +/- 2?

Then why do we have to keep remembering that the sq rt of something can either be positive or negative?

I know this might come as a source of confusion so let me clarify it well:

The square root symbol means, in fact, the +ve square root of. That's a definition and sometimes we just drop the word "positive" to say simply "the square root of".

Regarding your equation \(x^2=4\) x can be +/- 2, we have 2 answers because of the x^2 and nothing else so that gives 2 answers: one is the positive square root of 4 (which is 2) and the other is the negative of the square root of 4 (which is -2).