NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 13:37 It is currently 27 Apr 2024, 13:37
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If xy > 0, is y/x + x/y > 2?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92958
Own Kudos [?]: 619472 [17]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:00
3
Kudos
14
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

60% (02:02) correct 40% (02:17) wrong based on 461 sessions
Hide Show timer Statistics
If \(xy > 0\), is \(\frac{y}{x} + \frac{x}{y} > 2\)?


(1) \(y = x - 1\)

(2) \(x = 2y\)

 

This question was provided by Math Revolution
for the Heroes of Timers Competition

 

ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
firas92
Current Student
Joined: 16 Jan 2019
Posts: 631
Own Kudos [?]: 1444 [10]
Given Kudos: 144
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Send PM
Reviews Badge
If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:10
9
Kudos
1
Bookmarks
\(\frac{x^2+y^2}{xy}>2\)

Since xy>0, we can multiply the stem by xy maintaining the same inequality and we know that neither x nor y can be 0

So, \(x^2+y^2>2xy\) or \(x^2+y^2-2xy>0\) or \((x-y)^2>0\)

So we need to find whether \((x-y)^2>0\), this will be true when x-y is not equal to 0

(1) \(y=x-1\)

So, \(x-y=1\) => We know that x-y is non zero

So Sufficient

(2) \(x=2y\)

Or, \(x-y=y\)

Since y is non zero, \((x-y)^2 > 0\)

Sufficient

Answer is (D)
General Discussion
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3455 [2]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:14
2
Kudos
xy > 0
--> Both x>0 & y>0 (OR) x<0 & y<0

(1) y = x - 1
Since both x & y are of same sign, Irrespective of their values, x/y + y/x will always be > 2

eg: x = 2, y = 1
--> 2/1 + 1/2 = 2.5 > 2

x = 5, y = 4
--> 5/4 + 4/5 = 1.25 + 0.8 = 2.05 > 2

Sufficient

(2) x = 2y
--> x/y = 2
--> x/y + y/x = 2 + 1/2 = 2.5 > 2

Sufficient

IMO Option D

Pls Hit Kudos if you like the solution
avatar
G
AvidDreamer09
Manager
Manager
Joined: 19 Apr 2017
Posts: 84
Own Kudos [?]: 133 [3]
Given Kudos: 40
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE:Operations (Hospitality and Tourism)
Send PM
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:18
3
Kudos
Question Stem
\(\frac{y}{x}+\frac{x}{y}>2\)
\(y^2+x^2>2xy\)
\(y^2+x^2-2xy>0\)
\((x-y)^2>0\)

From Statement 1 \(x-y=1\) -> square both sides
\((x-y)^2=1\) sufficient

From Statement 2 \(x=2y\)
\(x/y=2\)
\(y/x=1/2\)
\(\frac{x}{y}+\frac{y}{x}=2+\frac{1}{2}\)

Which is greater than 2, hence sufficient

Answer D
User avatar
G
BelalHossain046
Manager
Manager
Joined: 11 Feb 2013
Posts: 202
Own Kudos [?]: 305 [3]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
Send PM
GMAT ToolKit User
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:18
2
Kudos
1
Bookmarks
Given, xy > 0 means neither x nor y can be ZERO
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13397 [3]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 08:28
3
Kudos
Expert Reply
Quote:
If xy>0, is y/x+x/y>2?


(1) y=x−1

(2) x=2y



If xy>0, i.e. signs of both x and y are identical
Now, y/x+x/y will be equal to 2 only if both x and y are equal otherwise it will always be greater than 2?
So question becomes

Is x = y?


(1) y=x−1

i.e. x and y are not equal hence SUFFICIENT

(2) x=2y

i.e. x and y are NOT equal hence SUFFICIENT

Answer: Option D
User avatar
G
Sayon
Manager
Manager
Joined: 08 Jan 2018
Posts: 84
Own Kudos [?]: 232 [3]
Given Kudos: 374
Send PM
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   03 Jul 2019, 22:03
3
Kudos
xy > 0, So x and y will have the same sign.
We are required to find whether \(\frac{y}{x}\) + \(\frac{x}{y}\) > 2
=> \(x^2 + y^2 > 2xy\)
=> \((x + y)^2 > 4xy\) -> [a]

(1) y = x -1
=> x = y + 1
Substituting the above value in [a] we get,
\((y + 1 + y)^2 > 4 (y + 1) y\)
=> \(4y^2 + 4y + 1 > 4y^2 + 4y\)
=> \(1 > 0\) This will always be true. Hence Sufficient

(2) x = 2y
Substituting the above value in [a] we get,
\((2y + y)^2 > 4 (2y) y\)
=> \(9y^2 > 8y^2\)
=> \(9 > 8\) This will always be true. Hence sufficient

Answer D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32715
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If xy > 0, is y/x + x/y > 2? [#permalink] New post   25 Jul 2022, 20:45
Hello from the GMAT Club BumpBot!

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.
GMAT Club Bot
gmatclubot
Re: If xy > 0, is y/x + x/y > 2? [#permalink]
25 Jul 2022, 20:45
Moderator:
Bunuel
Math Expert
92956 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions