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

 It is currently 17 Aug 2018, 02:58

### 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

# Is x a positive integer? (1) The reciprocal of x is greater than x

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47951
Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

25 Dec 2016, 02:41
00:00

Difficulty:

85% (hard)

Question Stats:

36% (01:04) correct 64% (01:03) wrong based on 205 sessions

### HideShow timer Statistics

Is x a positive integer?

(1) The reciprocal of x is greater than x
(2) x > | y |

_________________
Manager
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 137
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 660 Q47 V34
GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)
Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

Updated on: 05 Jan 2017, 23:08
Bunuel wrote:
Is x a positive integer?

(1) The reciprocal of x is greater than x
(2) x > | y |

Quote:
Q: X>0?

1) 1/x>x --> 1/2>2 --> NO (SUFFICIENT) 1) x<+/-1 -- INSUFFICIENT
2) X>|y| --> X>+veY --> YES (SUFFICIENT)
Hence DB.

Revision:
1) Only with negative numbers, the reciprocal si always greater than the number itself. So, the answer is NO. --> Sufficient.
2) x>+/-y. It can be either positive or negative. Two possibilities. So, the answer is YES or NO. --> Insufficient.

A.
_________________

Yours,
Siva Rama Krishna Meka

Originally posted by Sirakri on 25 Dec 2016, 02:54.
Last edited by Sirakri on 05 Jan 2017, 23:08, edited 1 time in total.
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

Updated on: 25 Dec 2016, 10:12
1
1
Bunuel wrote:
Is x a positive integer?

(1) The reciprocal of x is greater than x
(2) x > | y |

(1) The reciprocal of x is greater than x

x can be either a negative integer or a positive fraction:

x = -4, 1/x = -1/4, -1/4 > -4 ------> 1/x > x

or

x = 1/2, 1/x = 2, 2 > 1/2 -------> 1/x > x

Sufficient.

(2) x > | y |

It tells us that x is always positive, because absolute value is always positive.

But it does not tell us is x integer or not. x can be 1, 2, 1/3 ... Even if y is an integer it does not mean that x should be. Insufficient.

(1) & (2) together. That gives us a fraction between 0 and 1. No positive integer can have inverse greater than itself. (2 > 1/2)

x = 1/3, 1/x = 3, 3 > 1/3 --------> 1/x > x. Sufficient.

Originally posted by vitaliyGMAT on 25 Dec 2016, 08:19.
Last edited by vitaliyGMAT on 25 Dec 2016, 10:12, edited 1 time in total.
Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

25 Dec 2016, 10:07
3
Option A)

Is X a positive integer?

I: $$\frac{1}{X} > X$$
Above condition can be true if-
: X = -ve number or X = proper fraction
:eg, $$X = -6; \frac{1}{X} = -\frac{1}{6} : \frac{1}{X} > X$$ . X is NOT positive hence, X is NOT a Positive Integer.
: or $$X = \frac{1}{9}; \frac{1}{X} = 9 : \frac{1}{X} > X$$ . X is NOT an integer hence, X is NOT a Positive Integer.
In both cases X is NOT a Positive Integer.
Sufficient.

II: X > |Y|
:This means X is positive, but doesn't say anything about whether it's an integer or not.
Insufficient.
_________________

Press Kudos if you liked the post!

Rules for posting - PLEASE READ BEFORE YOU POST

Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

25 Dec 2016, 10:15
RR88 wrote:
Option A)

Is X a positive integer?

I: $$\frac{1}{X} > X$$
Above condition can be true if-
: X = -ve number or X = proper fraction
:eg, $$X = -6; \frac{1}{X} = -\frac{1}{6} : \frac{1}{X} > X$$ . X is NOT positive hence, X is NOT a Positive Integer.
: or $$X = \frac{1}{9}; \frac{1}{X} = 9 : \frac{1}{X} > X$$ . X is NOT an integer hence, X is NOT a Positive Integer.
In both cases X is NOT a Positive Integer.
Sufficient.

II: X > |Y|
:This means X is positive, but doesn't say anything about whether it's an integer or not.
Insufficient.

Answer is A, you are right. It seems I overworked
Intern
Joined: 12 Jun 2016
Posts: 27
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE: Information Technology (Computer Software)
Re: Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

25 Dec 2016, 22:46
One more method to solve:
1) 1/X > X
Then, multiplying both sides by X^2(this will always be +ve. So, we multiply it on both side of inequality).
X>X^3
(X^3 - X)<0
X(X^2-1)<0
X(X+1)(X-1)<0
The above inequality will be satisfied by: X<-1 and 0<X<1
Hence, we can conclude that X is not a positive integer. Sufficient.

2) X>|Y|
In this case, no information whether Y is integer or not. Not sufficient.

Ans- A.
Manager
Joined: 12 Oct 2015
Posts: 219
GMAT 1: 700 Q47 V39
GPA: 3
WE: Accounting (Accounting)
Re: Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

04 Jan 2017, 08:52
Bunuel wrote:
Is x a positive integer?

(1) The reciprocal of x is greater than x
(2) x > | y |

Excellent question, simple yet deceptive. Like many people I got negative integer and fraction and looked at (2) and immediately concluded C only to realize that both negative integer & a fraction do not meet the definition of positive integer. Awesome!
_________________

Winners dont make excuses.

350--> 700

https://gmatclub.com/forum/700-q47-v39-ir-7-awa-246682.html

Intern
Joined: 17 Sep 2016
Posts: 44
GMAT 1: 640 Q44 V35
Re: Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

04 Jan 2017, 09:40
Got 1st correct by using -ve number to meet condition & then comparing.
But 2nd made me think, absolute value is +ve !! Also, understood integer criteria by other replies.
Kudos.

Sent from my Lenovo A7020a48 using GMAT Club Forum mobile app
Intern
Joined: 07 Aug 2017
Posts: 2
Re: Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

10 Jun 2018, 05:12
Fairly simple trick question. Wonder why the difficulty shows 85%
Intern
Joined: 02 Nov 2017
Posts: 22
Location: India
Concentration: General Management, Finance
Schools: ISB
GMAT 1: 690 Q50 V35
GPA: 3.31
WE: General Management (Energy and Utilities)
Is x a positive integer? (1) The reciprocal of x is greater than x  [#permalink]

### Show Tags

12 Jul 2018, 03:21
Bunuel wrote:
Is x a positive integer?

(1) The reciprocal of x is greater than x
(2) x > | y |

Statement(1): 1/x>x, so x can be -ve integer less than -1 or positive fraction. not sufficient
statement(2): x>|y|.....so x is always positive.

Ans B
Is x a positive integer? (1) The reciprocal of x is greater than x &nbs [#permalink] 12 Jul 2018, 03:21
Display posts from previous: Sort by

# Is x a positive integer? (1) The reciprocal of x is greater than x

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

# Events & Promotions

 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®.