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:

The next set of medium/hard PS algebra questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers.

1. If \(x=\sqrt[4]{x^3+6x^2}\), then the sum of all possible solutions for x is:

4) -3x^2 + 12x -2y^2 - 12y - 39 MAX -3x^2 + 12x has max in (2,12) -2y^2 - 12y - 39 has max in (-6,-3) -3x^2 + 12x -2y^2 - 12y - 39 MAX = 12 - 3 =9 D _________________

It is beyond a doubt that all our knowledge that begins with experience.

@Bunuel, for Q5, shouldn't the original question also say that we are only looking for solutions where x is an integer?

For this to be satisfied, in x^2 + 2x -15 = -m, 4 - 4(m-15)>0 and 4-4(m-15) must be a perfect square => 4 (16-m) must be a perfect square and >0 => 16-m must be a perfect square and >0 The only values that satisfy this for -10<=m<=10 are m=-9,0,7 of which only 7 is positive => probability = 1/3 _________________

2. The equation x^2 + ax - b = 0 has equal roots, and one of the roots of the equation x^2 + ax + 15 = 0 is 3. What is the value of b?

A. -64 B. -16 C. -15 D. -1/16 E. -1/64

Let the roots of \(x^2 + ax +b = 0\) are h and h

So sum of the roots i.e \(2h = -a\) and product of the roots i.e \(h^2 = -b\) Now one root of \(x^2 + ax + 15=0\) is 5 So the other root must be 5 as the product is 15. So \(a = - (5+3) = -8\)

So, \(8 = 2h\) or, \(h=4\) So \(b = -4^2 = -16\) B it is _________________

5. If x^2 + 2x -15 = -m, where m is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?

A. 2/7 B. 1/3 C. 7/20 D. 2/5 E. 3/7

x^2 + 2x - 15 =-m or x^2 + 2x + (m-15) = 0 or (x+5)(x-3) = -m Now since m is an integer so x must also be an integer. x=1 m= 12 NO x=2 m= 7 YES x=3 m= 0 YES x=4 m= -9 YES x=5 m= -20 NO No further values will satisfy! So m has 3 values so far! x= 0 m= 15 NO x= -1 m= 16 NO x= -2 m= 15 NO x= -3 m= 12 NO x= -4 m= 7 YES x= -5 m= 0 YES x= -6 m= -9 YES x= -7 m= -20 NO

SO m can take 3 values 7, 0 and -9 and only ONE of them is greater than 0 SO the probability is 1/3 B _________________

Hey Bunuel! I touched quant after 3 months and I am really out of shape and its 2:30 in the morning! So If i answer incorrectly its partly my brain's fault! Oh well, when it isn't! _________________

4. What is the maximum value of -3x^2 + 12x -2y^2 - 12y - 39 ?

A. -39 B. -9 C. 0 D. 9 E. 39

differentiating with respect to x and equating with 0

\(-6x + 12 = 0, OR x=2\)

differentiating with respect to y and equating with 0

\(-4y - 12 =0, OR y=-3\)

So max value of the expression \(-3x^2 + 12x -2y^2 - 12y - 39\) is at (2, -3) i.e -12+24-18+36-39 = -9 B

Hi Souvik I liked ur approach cn u pls expand on it...i mean is there any hard and fast rule that u r following.....completely missed this question....

4. -3x^2 + 12x -2y^2 - 12y - 39 = -3x^2+12x-12-2y^2-12y-18-39+18+12 = -3(x-2)^2-2(y+3)^2 -9. Now a negative sign is attached to both the squares. Thus the maximum value is at x=2 and y=-3 and equals -9.

4. What is the maximum value of -3x^2 + 12x -2y^2 - 12y - 39 ?

A. -39 B. -9 C. 0 D. 9 E. 39

differentiating with respect to x and equating with 0

\(-6x + 12 = 0, OR x=2\)

differentiating with respect to y and equating with 0

\(-4y - 12 =0, OR y=-3\)

So max value of the expression \(-3x^2 + 12x -2y^2 - 12y - 39\) is at (2, -3) i.e -12+24-18+36-39 = -9 B

Hi Souvik I liked ur approach cn u pls expand on it...i mean is there any hard and fast rule that u r following.....completely missed this question....

Archit

I used calculus maxima minima. However you are free to use the "completing the square" method where you are left with 2 perfect squares and a -9 as the guy above me did. _________________

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...