GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 Jun 2018, 02:50

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If xy>0, which of the following must be positive?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46335
If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 11 May 2017, 03:03
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (01:01) correct 33% (01:03) wrong based on 212 sessions

HideShow timer Statistics

If xy>0, which of the following must be positive?


A. \((\sqrt{xy})^2x^3y^2\)

B. \((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2\)

C. \((\sqrt{xy})x^7y^9\)

D. \((\sqrt[3]{x^2y})x^2y^4\)

E. \((\sqrt{x^3y^5})x^2y^5\)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 610
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post Updated on: 11 May 2017, 05:04
Bunuel wrote:
If xy>0, which of the following must be positive?


A. \((\sqrt{xy})^2x^3y^2\)

B. \((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2\)

C. \((\sqrt{xy})x^7y^9\)

D. \((\sqrt[3]{x2y})x^2y^4\)

E. \((\sqrt{x3y5})x^2y^5\)


xy > 0
So either x>0, y>0 OR x<0, y<0
A. \((\sqrt{xy})^2x^3y^2\) = \(x^4 * y^3\) so -ve value is possible if y<0, x<0

B. \((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2\) = \((\sqrt[3]{x})(\sqrt[5]{y})(xy)^2x\)
For this option if y<0, x<0, \((\sqrt[3]{x})\) is +ve , \((\sqrt[5]{y})\) is -ve \(x^2y^2\) is -ve & x is -ve. So overall value is -ve.

C. \((\sqrt{xy})x^7y^9\) = \((\sqrt{xy})(xy)^7y^2\).. All the terms are +ve. So overall +ve.

D. \((\sqrt[3]{x2y})x^2y^4\) = \((\sqrt[3]{xy*y})x^2y^4\) . So if y <0 & x<0, \((\sqrt[3]{xy*y})\) is -ve and hence overall -ve is possible.

E. \((\sqrt{x3y5})x^2y^5\) = \((\sqrt{(xy)^3*y^2})(xy)^2y^3\) (+ve) * (+ve) *(-ve) is y<0 & x<0


Answer C

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".


Originally posted by shashankism on 11 May 2017, 04:23.
Last edited by shashankism on 11 May 2017, 05:04, edited 2 times in total.
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2846
Location: India
GPA: 3.12
Premium Member
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 11 May 2017, 04:43
There are 2 possibilities when xy > 0.
1. Both x and y are positive
2. Both x and y are negative

The only possibility in the answer choices which is definitely positive is Option C
Both the exponents of x and y are odd powers and since both of them are negative,
the expression will yield a positive answer(Option C)
_________________

You've got what it takes, but it will take everything you've got

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 15 May 2017, 17:26
Bunuel wrote:
If xy>0, which of the following must be positive?


A. \((\sqrt{xy})^2x^3y^2\)

B. \((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2\)

C. \((\sqrt{xy})x^7y^9\)

D. \((\sqrt[3]{x2y})x^2y^4\)

E. \((\sqrt{x3y5})x^2y^5\)


We are given that xy > 0, which means either x and y are both positive or both negative.

Scanning our answer choices, we see that only answer choice C MUST BE positive.

Since we know that xy is greater than zero, we know that √xy must also be greater than zero.

So, we have:

(positive)(x^7)(y^9)

Since xy is greater than zero, we see that (x^7)(y^9) = (x^7)(y^7)(y^2) = (xy)^7(y^2) must also be greater than zero.

Thus, (√xy)(x^7)(y^9) is greater than zero.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
User avatar
S
Status: Gmat lover
Joined: 27 Mar 2017
Posts: 87
Location: India
Schools: IIMA , IIMA PGPX"18
GMAT 1: 710 Q49 V39
GPA: 3.91
Reviews Badge
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 16 May 2017, 13:03
Bunuel Can you please tell me how can D be negative ,

I am stuck between C and D.
_________________

_________________
Rules for posting in verbal Gmat forum, read it before posting anything in verbal forum
Giving me + 1 kudos if my post is valuable with you :)

The more you like my post, the more you share to other's need.

“The great secret of true success, of true happiness, is this: the man or woman who asks for no return, the perfectly unselfish person, is the most successful.”
-Swami Vivekananda

Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1393
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 16 May 2017, 20:38
Bunuel wrote:
If xy>0, which of the following must be positive?


\(xy > 0 \implies x > 0 \; \text{and}\; y > 0 \quad \text{or} \quad x < 0 \;\text{and}\; y< 0 \)

A. \((\sqrt{xy})^2x^3y^2\)
\((\sqrt{xy})^2 > 0 \quad \forall xy > 0\)
\(x^3y^2=(xy)^2 \times x\)

If \(x < 0 \implies x^3y^2 < 0 \implies (\sqrt{xy})^2x^3y^2 < 0\)
Eliminated.

B. \((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2\)

\((\sqrt[3]{x})(\sqrt[5]{y})x^3y^2=(x)^{\frac{1}{3}}(y)^{\frac{1}{5}}x^3y^2=(x)^{\frac{10}{3}}(y)^{\frac{11}{5}} \)
\(=(x)^{\frac{10}{3}}(y)^{\frac{10}{5}} \times (y)^{\frac{1}{5}} \)
\(= \Big ( (x)^{\frac{1}{3}}(y)^{\frac{1}{5}} \Big ) ^{10} \times (y)^{\frac{1}{5}}\)

If \(y < 0 \implies (y)^{\frac{1}{5}} < 0 \implies \Big ( (x)^{\frac{1}{3}}(y)^{\frac{1}{5}} \Big ) ^{10} \times (y)^{\frac{1}{5}} < 0\)

Eliminated.

C. \((\sqrt{xy})x^7y^9\)
\((\sqrt{xy})x^7y^9 = (xy)^{\frac{1}{2}}(xy)^7y^2 \)
We have \(\sqrt{xy} > 0\)
\((xy)^7 > 0\) because \(xy>0\)
\(y^2 > 0\) because \(y \neq 0\)

Hence \((\sqrt{xy})x^7y^9 > 0\). This is the correct answer.

D. \((\sqrt[3]{x^2y})x^2y^4\)
\((\sqrt[3]{x^2y})x^2y^4=\sqrt[3]{x^2}\times\sqrt[3]{y}\times x^2y^4\)

If \(y < 0 \implies \sqrt[3]{y} < 0 \implies \sqrt[3]{x^2}\times\sqrt[3]{y}\times x^2y^4 < 0\).

Eliminated.

E. \((\sqrt{x^3y^5})x^2y^5\)
\(\sqrt{x^3y^5} \times x^2y^5 = \sqrt{(xy)^3 \times y^2}\times (xy)^2y^3 = \sqrt{(xy)^3} \times \sqrt{y^2} \times (xy)^2y^3 = \sqrt{(xy)^3} \times |y| \times (xy)^2y^3\)

Note that \(\sqrt{(xy)^3} > 0\) and \((xy)^2 > 0\) and \(|y| > 0\).

If \(y < 0 \implies y^3 < 0 \). Hence this choice is wrong.

The answer is C.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Intern
Intern
avatar
B
Joined: 11 Feb 2017
Posts: 24
Location: India
Schools: SPJ PGPM"17
GMAT 1: 600 Q48 V25
GPA: 3.57
WE: Engineering (Computer Software)
Reviews Badge
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 17 May 2017, 02:40
xy > 0
So either x>0, y>0 OR x<0, y<0
A. if y<0, x<0
(xy−−√)2x3y2(xy)2x3y2 = x4∗y3x4∗y3 so -ve value is possible

B. (x√3)(y√5)x3y2(x3)(y5)x3y2 = (x√3)(y√5)(xy)2x(x3)(y5)(xy)2x
For this option if y<0, x<0, (x√3)(x3) is +ve , (y√5)(y5) is -ve x2y2x2y2 is -ve & x is -ve. So overall value is -ve.

C. All the terms are +ve.

D. (x2y−−−√3)x2y4(x2y3)x2y4 = (xy∗y−−−−−√3)x2y4(xy∗y3)x2y4 . So if y <0 & x<0, (xy∗y−−−−−√3)(xy∗y3) is -ve and
hence -ve is possible.

E. (x3y5−−−−√)x2y5(x3y5)x2y5 = ((xy)3∗y2−−−−−−−−√)(xy)2y3((xy)3∗y2)(xy)2y3 (+ve) * (+ve) *(-ve) is y<0 & x<0 -ve is possible


Option C is correct.
Intern
Intern
avatar
B
Joined: 24 Aug 2013
Posts: 11
GMAT 1: 710 Q50 V36
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 20 May 2017, 22:38
I wrongly chose answer E.
My explanation is: squareroot(x^3*y^5)*x^2*y*5= x^3/2*y^5/2*x^2*y^5= x^7/2*y*15/2=squareroot(x^7*y^15)=squareroot(x^7*y^7*y^8).
Since xy>0 => (xy)^7>0 and y^8> 0
=> E has to be positive.
Can you pls explain?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46335
Re: If xy>0, which of the following must be positive? [#permalink]

Show Tags

New post 21 May 2017, 01:44
sayiurway wrote:
I wrongly chose answer E.
My explanation is: squareroot(x^3*y^5)*x^2*y*5= x^3/2*y^5/2*x^2*y^5= x^7/2*y*15/2=squareroot(x^7*y^15)=squareroot(x^7*y^7*y^8).
Since xy>0 => (xy)^7>0 and y^8> 0
=> E has to be positive.
Can you pls explain?


Say x = y = -1, then E. \((\sqrt{x^3y^5})x^2y^5=-1=negative\).

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: If xy>0, which of the following must be positive?   [#permalink] 21 May 2017, 01:44
Display posts from previous: Sort by

If xy>0, which of the following must be positive?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.