Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 15:59

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are nonzero integers, is x^y < y^x? (1) x =

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 26 Jul 2005
Posts: 315
Location: Los Angeles
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink] New post 27 Oct 2005, 15:28
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

69% (02:01) correct 31% (00:46) wrong based on 98 sessions
If x and y are nonzero integers, is x^y < y^x?

(1) x = y^2
(2) y > 2
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 20 Mar 2005
Posts: 202
Location: Colombia, South America
Followers: 1

Kudos [?]: 5 [0], given: 0

GMAT Tests User
 [#permalink] New post 27 Oct 2005, 16:04
I would pick A

x = y^2

so y^2^y = y^y^2 which i think is

y^2y = y^2y

so they are equal and you can answer the question
Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2005
Posts: 487
Followers: 1

Kudos [?]: 1 [0], given: 0

GMAT Tests User
 [#permalink] New post 27 Oct 2005, 16:32
i think its C

y^2y < y^y2

2y < y2

1 is Insuff b/c if y<=2, the answer is no, whereas when y>2, the answer is yes.

2) alone is insuff b/c it doesn't say anything about x (we need to know whether it is greater or less than 2.

Together, they are SUFF.
C
Director
Director
avatar
Joined: 24 Oct 2005
Posts: 577
Location: NYC
Followers: 1

Kudos [?]: 7 [0], given: 0

GMAT Tests User
 [#permalink] New post 28 Oct 2005, 11:48
A
coz 1 ^2 < 1 ^2 .. No it is not.. False and it stands false for anyother value too.
Manager
Manager
avatar
Joined: 01 Aug 2005
Posts: 68
Followers: 1

Kudos [?]: 2 [0], given: 0

 [#permalink] New post 28 Oct 2005, 12:43
Quote:
coz 1 ^2 < 1 ^2 .. No it is not.. False and it stands false for anyother value too.


I dont think its A, here is my reasoning.

Q: is x^y < y^x?

(1) x = y^2

if x is 4 and y is -2, statement 1 is correct but look at what happens.

4^-2 < -2^4
statement is now TRUE

if x is 4 and y is 2
4^2 < 2^4
statement is not true - they are equal.
Manager
Manager
avatar
Joined: 01 Aug 2005
Posts: 68
Followers: 1

Kudos [?]: 2 [0], given: 0

 [#permalink] New post 28 Oct 2005, 17:28
Valley,

I agreed with C, knew it couldnt be A because of 2 and 4. Would be nice to see the OE though just to see whether we all thought the right way.
Senior Manager
Senior Manager
avatar
Joined: 26 Jul 2005
Posts: 315
Location: Los Angeles
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
 [#permalink] New post 28 Oct 2005, 21:34
xennie - here is the OE...

It is helpful to note that (x^r)^s = x^(rs)

(1) From this, x = y^2, so by substitution then x^y = (y^2)^y or y^(2y), and y^x = y^(y^2). Comparing x^y to y^x can then be done by comparing y^(2y) to y^(y^2), or simply comparing the exponents 2y to y^2. If, for example, y = 2, then 2y = 4 and y^2 = 4, and then x^y would equal y^x. If, however, y = 3, then 2y = 6 and y^2 = 9, and so x^y would be less than y^x; NOT SUFFICIENT.

(2) It is known that y > 2, but no information about x is given; NOT SUFFICIENT.

If both (1) and (2) are taken together, then 2y is compared to y^2 (1) and from (2) it is known that y > 2, so 2y will always be less than y^2. Therefore, x^y < y^x.

<b>The correct answer is C.</b>
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 41 [0], given: 32

GMAT Tests User
Re: Exponents/inequalities problem from QR 2nd DS 121 [#permalink] New post 04 Aug 2010, 05:21
This is a tricky question. I think it relies on you misapplying the rule: (x^a)^b = x^{ab}. Is this only valid if a and b are constants?

Example:
(1) x = y^2;

x^y < y^x therefore, (y^2)^y < y^{y^2}. How do you simplify this? The guide shows to y^{2y} < y^{y^2}. The left hand side makes sense to me.

Why would y^{y^2} not simplify to y^{2y} also? Plugging in numbers, it makes sense. I just want to understand the concept.
Expert Post
9 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [9] , given: 2601

Re: Exponents/inequalities problem from QR 2nd DS 121 [#permalink] New post 04 Aug 2010, 05:52
9
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
jpr200012 wrote:
If x and y are nonzero integers, is x^y < y^x?

(1) x = y^2
(2) y > 2


If x and y are nonzero integers, is x^y < y^x?

(1) x = y^2 --> if x=y=1, then x^y=1=y^x, so the answer would be NO BUT if y=3 and x=9, then x^y=9^3<y^x=3^9, so the answer would be YES. Not sufficient.

(2) y>2. No info about x, not sufficient.

(1)+(2) From (1) x = y^2, thus the question becomes: is (y^2)^y<y^{(y^2)}? --> is y^{2y}<y^{(y^2)}? Now, since from (2) y=integer>2, then 2y will always be less than y^2, therefore y^{2y} will be less than y^{(y^2)}. Sufficient.

Answer: C.


jpr200012 wrote:
This is a tricky question. I think it relies on you misapplying the rule: (x^a)^b = x^{ab}. Is this only valid if a and b are constants?

Example:
(1) x = y^2;

x^y < y^x therefore, (y^2)^y < y^{y^2}. How do you simplify this? The guide shows to y^{2y} < y^{y^2}. The left hand side makes sense to me.

Why would y^{y^2} not simplify to y^{2y} also? Plugging in numbers, it makes sense. I just want to understand the concept.


If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
a^m^n=a^{(m^n)} and not (a^m)^n, which on the other hand equals to a^{mn}.

So:
(a^m)^n=a^{mn};

a^m^n=a^{(m^n)} and not (a^m)^n.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 24 Jul 2007
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: Exponents/inequalities problem from QR 2nd DS 121 [#permalink] New post 05 Aug 2010, 01:25
Posting this msg here even though i sent a private msg to you-for the benefit of others here.

Hi Bunuel, apprecite ur wonderful explanation. I am having trouble in DS question where x & y are termed as non-zero integers.

What is the best way to analyze instances where x & y are are NEGATIVE integers. I see that u have not analyzed this possibility. is there a trick to be sure that this is not needed as u have solved in this case?

Please enlighten. Thanks.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18683
Followers: 3232

Kudos [?]: 22200 [1] , given: 2601

Re: Exponents/inequalities problem from QR 2nd DS 121 [#permalink] New post 05 Aug 2010, 02:12
1
This post received
KUDOS
Expert's post
ramanankris wrote:
Posting this msg here even though i sent a private msg to you-for the benefit of others here.

Hi Bunuel, apprecite ur wonderful explanation. I am having trouble in DS question where x & y are termed as non-zero integers.

What is the best way to analyze instances where x & y are are NEGATIVE integers. I see that u have not analyzed this possibility. is there a trick to be sure that this is not needed as u have solved in this case?

Please enlighten. Thanks.


On DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

For statement (1) I got YES answer and then NO answer with positive numbers, so my goal to prove that this statement was not sufficient was reached, hence there was no need to try negative numbers.

Hope it's clear.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 24 Jul 2007
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: Exponents/inequalities problem from QR 2nd DS 121 [#permalink] New post 10 Aug 2010, 01:34
Thanks Bunuel, you are an inspiration.
VP
VP
User avatar
Status: Current Student
Joined: 24 Aug 2010
Posts: 1346
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 94

Kudos [?]: 399 [0], given: 73

Premium Member
Re: Is, x^y<y^x? [#permalink] New post 25 May 2011, 10:54
The answer is C

Statement 1: Insufficient

x=y^2 tells us that x is positive, but it tells us nothing about y.

For example if y=1 then x=1. Therefore 1^1=1^1 and x^y=y^x
If y=-2 then x=4. Therefore 4^-2<-2^4
Since we cannot get a definite yes or no from this statement, it is INSUFFICIENT

Statement 2: Insufficient
y>2
This tells us nothing about x.
If x=-1 and y=4, then -1^4>4^-1
If x=5 and y=3, then 5^3<3^5
Since we cannot get a definite yes or no from this statement, it is INSUFFICIENT

Putting both statements together we know that y>2 and x=y^2
If y=4, then x=16, then 16^4<4^16 (16^4 = 4^8).
No matter which integers you choose x^y < y^x, so Statements 1 and 2 together are SUFFICIENT. The answer is C.

_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com
Image

VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1365
Followers: 10

Kudos [?]: 131 [0], given: 10

GMAT Tests User
Re: Is, x^y<y^x? [#permalink] New post 26 May 2011, 00:03
a check for y = +|-1 and x = 1. giving different values for the equation.
Hence not sufficient.

b check for y = 3 and x = -1 | 9 giving different values for the equation.
Not sufficient.

a+b

y=3, x= 9
y=4 x = 16 give same value meaning LHS = RHS in fact.

hence C.

_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 447
Schools: Kelley,Tepper,Carlson,Kenan Flager,Broad
Followers: 4

Kudos [?]: 103 [0], given: 22

GMAT Tests User
Re: Is, x^y<y^x? [#permalink] New post 26 May 2011, 00:04
if x and y are nonzero integers is, x^y < y^x?
(1) x = y^2
(2) y > 2

x^y < y^x
Stmt1: x=y^2
x^y ---> y^2^y= y^(2y)
y^x ---> y^(y^2)
Is y^(2y) < y^(y^2) ?
Take log both side
2y logy < y^2logy ?
Canceling log y
Is 2y < y^2 ?
Is 2<y ? i.e Is y>2?
We don't know the value of y. Hence not sufficient.

Stmt2: y>2
Not sufficient.

Combining, from Stmt2: we know that y>2 .
Hence Stmt1: Is y>2 can be answered taking Stmt1 and Stmt2 together.

OA C.

_________________

My dad once said to me: Son, nothing succeeds like success.

VP
VP
User avatar
Status: Current Student
Joined: 24 Aug 2010
Posts: 1346
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 94

Kudos [?]: 399 [0], given: 73

Premium Member
Re: Is, x^y<y^x? [#permalink] New post 26 May 2011, 03:10
jamifahad wrote:
if x and y are nonzero integers is, x^y < y^x?
(1) x = y^2
(2) y > 2

x^y < y^x
Stmt1: x=y^2
x^y ---> y^2^y= y^(2y)
y^x ---> y^(y^2)
Is y^(2y) < y^(y^2) ?
Take log both side
2y logy < y^2logy ?
Canceling log y
Is 2y < y^2 ?
Is 2<y ? i.e Is y>2?
We don't know the value of y. Hence not sufficient.

Stmt2: y>2
Not sufficient.

Combining, from Stmt2: we know that y>2 .
Hence Stmt1: Is y>2 can be answered taking Stmt1 and Stmt2 together.

OA C.

Nice solve. However, GMAT Math does not require the knowledge of logarithms. Definitely can help on the test, but for people who haven't touched a logarithm since high school it's not necessary to relearn them to answer this question.

_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com
Image

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2049
Followers: 125

Kudos [?]: 873 [0], given: 376

GMAT Tests User
Re: Is, x^y<y^x? [#permalink] New post 26 May 2011, 03:43
jamifahad wrote:
Is 2y < y^2 ?
Is 2<y ? i.e Is y>2?


The rephrase is not complete.

2y<y^2
y^2-2y>0
y(y-2)>0

************************
If y>0; y-2>0;
Is y>2
OR
y<0
***********************

However, "y<0" actually doesn't hold true for x^y<y^x (for y=-1)
*********************

The only point I am trying to make here is that solving through logarithm may give us undesired results. What if x^y or y^x is negative. Then, taking the logarithms would be wrong!!!

*******************************************

_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 447
Schools: Kelley,Tepper,Carlson,Kenan Flager,Broad
Followers: 4

Kudos [?]: 103 [0], given: 22

GMAT Tests User
Re: Is, x^y<y^x? [#permalink] New post 27 May 2011, 01:21
On another look,
From stmt1: x=y^2, soy=\sqrt{x}. Since \sqrt{x}will always be a positive number, y will always be positive.
Substituting, in x^y < y^x,
x^sqrt(x) < \sqrt{x} ^ x
Now we can safely take log as both sides are positive.
sqrt(x)logx < xlog sqrt(x)
sqrt(x) logx < x/2 log x
Is sqrt(x) < x/2 ?
Is 2 < sqrt(x) ?
Cannot be determined. Not sufficient.

Stmt2: y>2. Not sufficient.

Combining, from stmt1 y=\sqrt{x}
From stmt2: y>2. i.e \sqrt{x} >2.
Hence 2 < sqrt(x) ? . Yes.

OA C.

_________________

My dad once said to me: Son, nothing succeeds like success.

VP
VP
User avatar
Status: Current Student
Joined: 24 Aug 2010
Posts: 1346
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 94

Kudos [?]: 399 [0], given: 73

Premium Member
Re: Is, x^y<y^x? [#permalink] New post 27 May 2011, 03:21
jamifahad wrote:
On another look,
From stmt1: x=y^2, soy=\sqrt{x}. Since \sqrt{x}will always be a positive number, y will always be positive.
Substituting, in x^y < y^x,
x^sqrt(x) < \sqrt{x} ^ x
Now we can safely take log as both sides are positive.
sqrt(x)logx < xlog sqrt(x)
sqrt(x) logx < x/2 log x
Is sqrt(x) < x/2 ?
Is 2 < sqrt(x) ?
Cannot be determined. Not sufficient.

Stmt2: y>2. Not sufficient.

Combining, from stmt1 y=\sqrt{x}
From stmt2: y>2. i.e \sqrt{x} >2.
Hence 2 < sqrt(x) ? . Yes.

OA C.

x=y^2, Just because x is positive doesn't mean y has to be positive. Even powers always yield a positive number, even if the base is negative.
For example, if x=4 then y can be 2 or -2. The only thing we can determine from statement 1 is that x is positive. y can be either positive or negative. If y is negative then x^y would be 1/x^y. 1/x^y may or may not be greater than y^x. y=-3, x=9 vs y=3, x=9. 1/9^3>-3^9. 9^3<3^9.

_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com
Image

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1704
Followers: 162

Kudos [?]: 33 [0], given: 0

Premium Member
Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink] New post 20 Jul 2014, 10:19
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If x and y are nonzero integers, is x^y < y^x? (1) x =   [#permalink] 20 Jul 2014, 10:19
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x and y are nonzero integers, is x^y < y^x ? Bunuel 3 03 Mar 2014, 23:14
If x and y are nonzero integers, is x^y < y^x? A. x=y^2 nfa1rhp 3 29 Jul 2007, 10:11
If x and y are nonzero integers, is x^y < y^x ? 1) x = DreamMBA 3 31 Dec 2006, 13:33
x and y are positive integers, is X^y <= Y^x? 1. X = y^2 M8 4 14 Aug 2006, 22:05
X and Y are non zero integers is x^y < y^x? 1)x=y^2 Rupstar 13 01 Mar 2005, 16:29
Display posts from previous: Sort by

If x and y are nonzero integers, is x^y < y^x? (1) x =

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.