It is currently 15 Jul 2020, 10:12

### GMAT Club Daily Prep

#### 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

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

# xy = 2 and x > 0 and y > 0

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 12125
Followers: 256

Kudos [?]: 3028 [1] , given: 11304

xy = 2 and x > 0 and y > 0 [#permalink]  08 Mar 2020, 10:42
1
KUDOS
Expert's post
00:00

Question Stats:

64% (00:31) correct 35% (00:36) wrong based on 62 sessions
$$xy = 2$$
$$x > 0$$
$$y > 0$$

 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
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3535
Followers: 134

Kudos [?]: 4020 [1] , given: 65

Re: xy = 2 and x > 0 and y > 0 [#permalink]  09 Mar 2020, 07:04
1
KUDOS
Expert's post
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

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com
Sign up for my free GRE Question of the Day emails

Intern
Joined: 08 Mar 2020
Posts: 13
Followers: 0

Kudos [?]: 13 [1] , given: 1

Re: xy = 2 and x > 0 and y > 0 [#permalink]  10 Mar 2020, 09:32
1
KUDOS
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 Mar 2020, 09:32
Display posts from previous: Sort by

# xy = 2 and x > 0 and y > 0

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.