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

Question

Is x a positive integer?

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

Sirakri · Answer

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.

vitaliyGMAT · Answer

(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.

Answer C

RR88 · Answer

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.

vitaliyGMAT · Answer

Answer is A, you are right. It seems I overworked :-D

shashank1tripathi · Answer

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.

jkolachi · Answer

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!

akhiparth · Answer

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

P@PU · Answer

Fairly simple trick question. Wonder why the difficulty shows 85%

durgamadhab · Answer

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

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

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

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