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.

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:

(1) w > 2. Subtract \(w > 2\) from \(wz < 2\) (we can do it as the signs are in opposite direction):

\(wz-w<2-2\) --> \(w(z-1)<0\), as w is positive (given w>2), then the product to be negative \(z-1\) must be negative --> \(z-1<0\) --> \(z<1\). Sufficient.

(2) z < 2. If \(z=1.5>1\) and \(w=0\) (wz<2), then the answer is YES but if \(z=0<1\) and \(w=0\) (wz<0), then the answer is NO. Not sufficient.

Here the simple way to conclude that statement 1 is sufficient is because w is always positive and greater than 2 for w=2 which it cant be => z=1 so as Z increases z will decrease => Z<1
_________________

Statement 1: w > 2 This means that w is POSITIVE, which means we can divide both sides of the given inequality, wz < 2, by w. We get: z < 2/w First, since w is POSITIVE, we know that 2/w is POSITIVE, which means z is POSITIVE Second, since w > 2, we know that 2/w will be less than 1, since the denominator is greater than the numerator So, we can write 2/w < 1 Since z < 2/w, we can write: z < 2/w < 1 This means we can conclude that z < 1 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z < 2 There are several values of w and z that satisfy statement 2 (and the given info). Here are two: Case a: w = 1 and z = 0. Notice that this satisfies the given info that wz < 2. In this case z < 1 Case b: w = 1 and z = 1.5. Notice that this satisfies the given info that wz < 2. In this case z > 1 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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.
_________________