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

 It is currently 15 Nov 2018, 15:42

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

# If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50613
If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

27 Oct 2005, 15:28
4
16
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:19) correct 35% (01:18) wrong based on 576 sessions

### HideShow timer Statistics

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

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

Data Sufficiency
Question: 121
Category: Arithmetic; Algebra Arithmetic operations; Inequalities
Page: 161
Difficulty: 650

The Official Guide For GMAT® Quantitative Review, 2ND Edition
Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

04 Aug 2010, 05:52
14
9
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.

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.
_________________
##### General Discussion
Manager
Joined: 30 May 2010
Posts: 179
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

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.
Intern
Joined: 24 Jul 2007
Posts: 4
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

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?

Math Expert
Joined: 02 Sep 2009
Posts: 50613
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

05 Aug 2010, 02:12
1
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?

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.
_________________
Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 490
Location: India
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

23 Feb 2017, 04:54
Prompt analysis
Let the number of tapes with carmen and rafael be x and y respectively.

x+12 = 2y

Superset
Value of x and y will be a whole number.

Translation
St 1: y =x +5. Solving 2 equations we get x = 2, y =7. ANSWER
St 2: x<12. Cannot determine the exact value of x. INSUFFICIENT

Option A
_________________

GMAT Mentors

Non-Human User
Joined: 09 Sep 2013
Posts: 8773
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2  [#permalink]

### Show Tags

10 Jul 2018, 05:18
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.
_________________
Re: If x and y are nonzero integers, is x^y < y^x ? (1) x = y^2 (2) y > 2 &nbs [#permalink] 10 Jul 2018, 05:18
Display posts from previous: Sort by