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

It is currently 10 Jul 2014, 07:25

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 n is a prime number greater than 2, is 1/x > 1?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 121
Followers: 1

Kudos [?]: 170 [0], given: 17

If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 21:03
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

23% (02:42) correct 76% (01:19) wrong based on 43 sessions
If n is a prime number greater than 2, is 1/x > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Last edited by MacFauz on 08 May 2013, 21:52, edited 1 time in total.
Formatted the question
Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 525 [1] , given: 135

Premium Member
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 23:41
1
This post received
KUDOS
Expert's post
emmak wrote:
If n is a prime number greater than 2, is 1/x > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


The question is asking, is \frac{1}{x}>1 --> Is 0<x<1

From F.S 1, for n=3, we havex^3<x<x^{\frac{1}{3}} . As x>x^3, we have x(1-x^2)>0 --> x(x+1)(x-1)<0 .

Hence 0<x<1 OR x<-1. Again, from x<x^{\frac{1}{3}}, we can cube on both sides and get, x^3<x, which is the same as above. Thus, from F.S 1, we get :

0<x<1 OR x<-1. Insufficient.

From F.S 2, we know that for n=3, x^2 > x^4 --> x^2<1 --> -1<x<1. Clearly Insufficient.

Taking both together, we get 0<x<1 as the common range and a YES for the question stem. Sufficient.

C.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
User avatar
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Followers: 11

Kudos [?]: 63 [0], given: 14

GMAT ToolKit User
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 22:28
emmak wrote:
If n is a prime number greater than 2, is 1/x > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


Couldn't the answer be [A],

Statement 1: for all n where n is prime and > 2, x^n < x < x^1/n.
Since n>2, n must be odd. Hence the above values of x belongs to {0,1} will hold for the above equation. For -ve values of x, x^1/n will not be defined.

In such a case, 1/x>1 or x belongs to {0,1} -ve values again will not satisfy the equation.

Statement 2: x^(n-1) > x^2(n-1), for n being odd, n-1 will be even. Hence for the above equation the solution set will be {-1,1}
As mentioned above, the negative values of x will not hold the 1/x>1 equation. Hence the range is again {0,1}.

Am I doing sumthing wrong?

Regards,
Arpan
_________________

Feed me some KUDOS! :) :) *always hungry*

My Thread : Recommendation Letters

Manager
Manager
User avatar
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 92
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 61 [0], given: 11

Reviews Badge
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 22:56
emmak wrote:
If n is a prime number greater than 2, is \frac{1}{x} > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


The Question asks ......Is \frac{1}{x}>1 ...... & this is only possible only if x is a +ve proper fraction .. where

Denominator is greater than the numerator. So in other words.. Question Asks ... Is X is a +ve proper fraction ?????

So, We have to find if X is a +ve Proper fraction or not ......

Given, N is a prime Number greater than 2.....

Statement :: 1 Says ..... x^n < x < x^{\frac{1}{n}} ....

This is only possible if x is a +ve proper fraction .. if you want to check .. plugin the value of n as 3 or 5 .... Therefore, from this ....

we can say that x is a +ve proper fraction.. Therefore. Sufficient ..


Statement :: 2 says ... x^{n-1} > x^{2n-2} ...

x^{n-1} > x^{2n-2}

It can be written as ... .... x^{n+1} > x^{2n}



Therefore.. InSufficient ....

Hence, ...... A.......
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.


Last edited by manishuol on 09 May 2013, 00:42, edited 3 times in total.
Manager
Manager
User avatar
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Followers: 11

Kudos [?]: 63 [0], given: 14

GMAT ToolKit User
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 23:14
manishuol wrote:
emmak wrote:
If n is a prime number greater than 2, is \frac{1}{x} > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


The Question asks ......Is \frac{1}{x}>1 ...... & this is only possible only if x is a proper fraction .. where

Denominator is greater than the numerator. So in other words.. Question Asks ... Is X a proper fraction ?????

So, We have to find if X is a Proper fraction or not ......

Given, N is a prime Number greater than 2.....

Statement :: 1 Says ..... x^n < x < x^{\frac{1}{n}} ....

This is only possible if x is a proper fraction .. if you want to check .. plugin the value of n as 3 or 5 .... Therefore, from this ....

we can say that x is a proper fraction.. Therefore. Sufficient ..


Statement :: 2 says ... x^{n-1} > x^{2n-2} ...

x^{n-1} > x^{2n-2}

In this one also if we plugin in the value of n as 3 or 5 ... we will get when n = 3 ...x^2 > x^4

& when n = 5 .. we will get x^4 > x^8 ....... Both of these states that x is a proper fraction .....

Therefore.. Sufficient ....

Hence, ...... D.......


I agree with Statement 1 being sufficient, but when it comes to Statement 2,

For example, x = -0.1, in such a case, assuming n is Odd and equal to 3, the inequality can be reduced to x^2>x^4. The value x = -0.1 satisfies.

Since the power term (n-1) will always be even, the inequality will hold good for even -ve numbers between {-1,0}. But when it comes to our parent equation:
1/-0.1 = -10 < 1. Hence the inequality doesn't satisfy. Therefore, I feel [A] should be the answer. Please look into my method and let me know if I am doing anything wrong! Also please refer to my post above for a general approach to the prob.

Regards,
Arpan
_________________

Feed me some KUDOS! :) :) *always hungry*

My Thread : Recommendation Letters


Last edited by arpanpatnaik on 08 May 2013, 23:35, edited 1 time in total.
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 525 [0], given: 135

Premium Member
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 23:45
Expert's post
arpanpatnaik wrote:
emmak wrote:
If n is a prime number greater than 2, is 1/x > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


Couldn't the answer be [A],

Statement 1: for all n where n is prime and > 2, x^n < x < x^1/n.
Since n>2, n must be odd. Hence the above values of x belongs to {0,1} will hold for the above equation. For -ve values of x, x^1/n will not be defined.


Not true. As x>2 and is a prime number, x will always be an odd integer. For x = -8,x^{1/3} = -2.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
User avatar
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 92
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 61 [0], given: 11

Reviews Badge
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 08 May 2013, 23:59
arpanpatnaik wrote:
manishuol wrote:
emmak wrote:
If n is a prime number greater than 2, is \frac{1}{x} > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


The Question asks ......Is \frac{1}{x}>1 ...... & this is only possible only if x is a proper fraction .. where

Denominator is greater than the numerator. So in other words.. Question Asks ... Is X a proper fraction ?????

So, We have to find if X is a Proper fraction or not ......

Given, N is a prime Number greater than 2.....

Statement :: 1 Says ..... x^n < x < x^{\frac{1}{n}} ....

This is only possible if x is a proper fraction .. if you want to check .. plugin the value of n as 3 or 5 .... Therefore, from this ....

we can say that x is a proper fraction.. Therefore. Sufficient ..


Statement :: 2 says ... x^{n-1} > x^{2n-2} ...

x^{n-1} > x^{2n-2}

In this one also if we plugin in the value of n as 3 or 5 ... we will get when n = 3 ...x^2 > x^4

& when n = 5 .. we will get x^4 > x^8 ....... Both of these states that x is a proper fraction .....

Therefore.. Sufficient ....

Hence, ...... D.......


I agree with Statement 1 being sufficient, but when it comes to Statement 2,

For example, x = -0.1, in such a case, assuming n is Odd and equal to 3, the inequality can be reduced to x^2>x^4. The value x = -0.1 satisfies.

Since the power term (n-1) will always be even, the inequality will hold good for even -ve numbers between {-1,0}. But when it comes to our parent equation:
1/-0.1 = -10 < 1. Hence the inequality doesn't satisfy. Therefore, I feel [A] should be the answer. Please look into my method and let me know if I am doing anything wrong! Also please refer to my post above for a general approach to the prob.

Regards,
Arpan



My answer is still A ...
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.


Last edited by manishuol on 09 May 2013, 00:34, edited 2 times in total.
Manager
Manager
User avatar
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Followers: 11

Kudos [?]: 63 [0], given: 14

GMAT ToolKit User
Re: If n is a prime number greater than 2, is 1/x > 1? [#permalink] New post 09 May 2013, 00:06
vinaymimani wrote:
arpanpatnaik wrote:
emmak wrote:
If n is a prime number greater than 2, is 1/x > 1?
(1) x^n < x < x^{\frac{1}{n}}
(2)x^{n-1} > x^{2n-2}


Couldn't the answer be [A],

Statement 1: for all n where n is prime and > 2, x^n < x < x^1/n.
Since n>2, n must be odd. Hence the above values of x belongs to {0,1} will hold for the above equation. For -ve values of x, x^1/n will not be defined.


Not true. As n>2 and is a prime number, will n always be an odd integer. For x = -8,x^{1/3} = -2.


My Bad!! I missed that... Thanks for correcting me Vinay! I got the answer now! [C] it is :)
Can't believe I used the odd principle in Statement 2 and failed to use it in Statement 1. The range x < -1 will be valid and the solution set needs to be an intersection of Statement 1 and 2 i.e. x belongs to {0,1}.

Regards,
Arpan
_________________

Feed me some KUDOS! :) :) *always hungry*

My Thread : Recommendation Letters

Re: If n is a prime number greater than 2, is 1/x > 1?   [#permalink] 09 May 2013, 00:06
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Is x^2>x (1) x^2 is greater than 1 (2) x is greater than -1 TomB 1 14 May 2012, 09:39
3 Experts publish their posts in the topic Is x > x^2 ? (1) x is greater than x^3 (2) x is greater t rxs0005 7 04 Feb 2012, 08:23
2 Is x-y+1 greater than x+y-1 1) x>0 2) y<0 Michmax3 6 30 Sep 2010, 21:11
Is x-y+1 greater than x+y-1 ? (1) x > 0 (2) y < 0 jpr200012 2 17 Aug 2010, 23:30
Is y greater than x? (1) |y|<1 and |x| <2 (2) y>0 aiming4mba 2 22 Jul 2010, 12:07
Display posts from previous: Sort by

If n is a prime number greater than 2, is 1/x > 1?

  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®.