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 GRE 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:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
xy = 2 and x > 0 and y > 0
[#permalink]
08 Mar 2020, 10:42
2
2
Expert Reply
8
Bookmarks
00:00
Question Stats:
64% (00:50) correct
35% (00:47) wrong based on 239 sessions
HideShow
timer Statistics
\(xy = 2 \) \(x > 0 \) \(y > 0 \)
Quantity A
Quantity B
\(x+y\)
\(5\)
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
xy = 2 and x > 0 and y > 0
[#permalink]
09 Mar 2020, 07:04
1
Carcass wrote:
\(xy = 2 \) \(x > 0 \) \(y > 0 \)
Quantity A
Quantity B
\(x+y\)
\(5\)
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Key concept: If we ASSUME that x and y are integers, we'll incorrectly conclude that quantity B is greater However, if we realize that x and y can be non-integers, we can quickly see that the correct answer must be D
To show why, let's test some values
case i: Since \(xy = 2 \), one possible pair of values is \(x=1\) and \(y=2\) We get: Quantity A: \(x+y=1+2=3\) Quantity B: \(5\) In this case, Quantity B is greater
case ii: Since \(xy = 2 \), another possible pair of values is \(x=8\) and \(y=0.25\) We get: Quantity A: \(x+y=8+0.25=8.25\) Quantity B: \(5\) In this case, Quantity A is greater
Re: xy = 2 and x > 0 and y > 0
[#permalink]
10 Mar 2020, 09:32
4
Using AM-GM inequality, we find that (x+y)/2 >= sqrt(xy), which implies x+y >= 2*sqrt(2) = 2.82...., which is less than 5. Also, notice that y=2/x. Hence, we can increase x indefinitely and since y is always positive as long as x is positive, x+y can go up to infinity. Since x+y can be greater than or less than 5 depending on the values of x and y, the correct option is D.
Re: xy = 2 and x > 0 and y > 0
[#permalink]
10 Aug 2024, 10:47
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep 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.