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:
Join a FREE 1-day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today!
The question cannot be easily rephrased to incorporate the particular information given. However, of course we should take note that both variables are integers and that \(x\) is less than \(y\). We are looking for the value of \(x + y\).
Statement (1): SUFFICIENT. First, we should list out all the possible scenarios in which integers \(x\) and \(y\) fit the equation \(x^y = 4\).
There are three possibilities, as we can find by trial and error: \(2^2 = 4\), \((-2)^2 = 4\), and \(4^1 = 4\). However, of these possibilities, there is only one for which \(x\) is less than \(y\), namely \((-2)^2 = 4\). Thus, we can find the value of \(x + y\), which is \(-2 + 2 = 0\).
Statement (2): SUFFICIENT. Knowing that \(|x| = |y|\) does not tell us the values of the integers. However, since they have the same absolute value, but \(x\) is less than \(y\), it must be the case that \(y\) is a positive integer and \(x\) is the negative of that integer. For instance, if \(y\) is 5, then \(x\) is -5. The sum of \(x\) and \(y\) must therefore be 0, no matter what.
I still don't understand how the second statement in sufficient.
If x and y are integers and x<y, what is the value of x+y?
(1) x^y=4 --> as x and y are integers and x<y then only possible solution is (-2)^2=4 (other integer solutions for x^y=4 are: 2^2=4 and 4^1=4) --> x+y=-2+2=0. Sufficient.
(2) |x|=|y| --> as also x<y then they have opposite signs (x<0<y, so |x|=-x and|y|=y) --> -x=y --> x+y=0. Sufficient.
I think this is a high-quality question and I agree with explanation. interesting ques, though got it wrong(chose option A) but learned a point.
_________________
close
30% (01:27) correct 
