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 350,000 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:

If y=root(3y+4), then the product of all possible solution [#permalink]
20 May 2010, 10:02

3

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

Prax wrote:

Can you please help me with this question:

If y=\sqrt{3y+4}, then the product of all possible solution(s) for y is: -4 -2 0 4 6

Square both sides: y^2=3y+4 --> (y+1)(y-4)=0 --> y=-1 or y=4, but y cannot be negative as it equals to square root of some expression (\sqrt{expression}\geq{0}), so only one solution is valid y=4.

Re: If y=root(3y+4), then the product of all possible solution [#permalink]
20 May 2010, 10:36

2

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

Prax wrote:

But don't we consider negative sq. root as well?

This issue was discussed several times lately on the forum and let me assure you: square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

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 non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, \sqrt[3]{125} =5 and \sqrt[3]{-64} =-4.

So when we see y=\sqrt{3y+4} we can deduce TWO things: A. y\geq{0} - as square root function can not give negative result; B. 3y+4\geq{0} - as GMAT is dealing only with real numbers and even roots of negative number is undefined (3y+4 is under square root so it must be \geq{0}).

Re: If y=root(3y+4), then the product of all possible solution [#permalink]
19 Apr 2013, 02:02

1

This post received KUDOS

rakeshd347 wrote:

noboru wrote:

If y=sqrt(3y+4) then the product of all possible solution(s) for y is

a -4 b -2 c 0 d 4 e 6

D is the correct answer. The two solutions are 4 and -1 then -1 doesn't satisfy the equation so the only solution is 4. D is correct.

Hello rakeshd347.,

If the two solutions are 4 and -1, that would mean that they both satisfy the equation and that is why they are the solutions. The product of all possible solutions is hence 4*-1 = -4.

If it helps, in an equation ax^2 + bx + c = 0, the sum of the roots is \frac{-b}{a} and the product of the roots is \frac{c}{a} _________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: If y=root(3y+4), then the product of all possible solution [#permalink]
12 May 2014, 00:10

Hello from the GMAT Club BumpBot!

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. _________________

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...