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:

We have a yes-no question, so we'll need to know if \(x\) is always prime or never prime. When working with primes, keep in mind that 2 is the smallest prime number on the only even prime. Other than that, all we know from the stem is that \(x > 0\), so let's evaluate the statements.

(1) Insufficient. Can we find any prime values for x such that \(x^3\) has 4 distinct factors? If \(x=2\), which is prime, then \(x^3 = 2^3 = 8\), which has 4 distict factors (1, ,2, 4, and 8). So it's possible that \(x\) is prime. But does it have to be prime? Lets consider other positive numbers with 4 distinct factors. The smalelst such number is 6 (its factors are 1, 2, 3, and 6), so suppose \(x^3 = 6\). In this case, \(x = \sqrt{6}\), which is not even an integer, much less a prime number. So we've found both prime and non-prime values for \(x\) that make (1) true. Therefore, (1) is insufficent to determine whether or not \(x\) is prime. Eliminate (A) and (D).

(2) Sufficient. In this case, we can solve the equation to find possible values for \(x\). If we subtract 6 from both sides, we get \(x^2 - x - 6 = 0\). Factor the left side using reverse FOIL to get (x-3)(x+2) = 0. So, the equation has one negative root and one positive root, meaning that there are two possible values for x, one negative and one positive. The stem tells us that \(x\) must be positive, so there is actually only one possible value of \(x\). Since we could find exactly one value for \(x\), we can answer the question definitely, if we know what \(x\) is, we know whether or not it is prime. So Statement (2) is sufficient. Answer B.
_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.