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# If x is an integer and x^2>1, is x a positive integer?

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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02 Sep 2018, 07:51
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Difficulty:

45% (medium)

Question Stats:

64% (01:15) correct 36% (01:23) wrong based on 149 sessions

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If x is an integer and $$x^2>1$$, is x a positive integer?

(1) $$x^2=6x$$

(2) $$x=|y|$$, where y is an integer

New question!!...

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Director
Joined: 18 Jul 2018
Posts: 675
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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02 Sep 2018, 07:58
1
From statement 1:

X^2-6X = 0
X(X-6) = 0
X = 0 or 6.

Since X^2>0 then X = 6.
1 is sufficient.

From statement 2: X = +Y or -Y.

Hence insufficient.

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Joined: 13 Jun 2017
Posts: 18
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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02 Sep 2018, 08:13
From statement 1:

We can say that x = 0 or 6.

Statement 1 is sufficient.

From statement 2:

|y| is always positive, therefore x is always positive.

Statement 2 is sufficient.

Director
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Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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02 Sep 2018, 09:36
1
chetan2u wrote:
If x is an integer and $$x^2>1$$, is x a positive integer?
(1) $$x^2=6x$$
(2) $$x=|y|$$, where y is an integer

New question!!...

Given, $$x^2>1$$ implies that |x|>1
Or, x < -1, x >1 (x: all the integers except -1,0,1)----------(a)

Question stem :- Is x>0 ?

St1:- $$x^2=6x$$
Or, $$x^2-6x=0$$
Or, x(x-6)=0
So, x=6,0--------------(b)
From (a)&(b), x=6.
Sufficient.

St2:- $$x=|y|$$, where y is an integer
Here |y| is an absolute expression, so x is always positive irrespective of sign of y. However, y may take +ve or -ve polarity.
Hence, x is positive.
Sufficient.
NOTE:- We have to discard the following possible values of y hence x.
1) y=0,1,-1; This as per our observation obtained at (a).

Ans. (D)
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Joined: 31 Oct 2013
Posts: 1154
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Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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02 Sep 2018, 13:46
[quote="Afc0892"]From statement 1:

X^2-6X = 0
X(X-6) = 0
X = 0 or 6.

Since X^2>0 then X = 6.
1 is sufficient.

From statement 2: X = +Y or -Y.

Hence insufficient.

Hey, In statement 2, x = |y|. u don't have to think about the value of y or it's sign. Regardless of y's sing , x is always positive.

Thanks.
Joined: 05 Mar 2017
Posts: 195
Concentration: Operations, General Management
Schools: Terry '21 (M\$)
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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03 Sep 2018, 02:42
1
selim wrote:
Afc0892 wrote:
From statement 1:

X^2-6X = 0
X(X-6) = 0
X = 0 or 6.

Since X^2>0 then X = 6.
1 is sufficient.

From statement 2: X = +Y or -Y.

Hence insufficient.

Hey, In statement 2, x = |y|. u don't have to think about the value of y or it's sign. Regardless of y's sing , x is always positive.

Thanks.

so it shud b "D" know?
Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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03 Sep 2018, 06:32
chetan2u wrote:
If x is an integer and $$x^2>1$$, is x a positive integer?
(1) $$x^2=6x$$
(2) $$x=|y|$$, where y is an integer

New question!!...

(1) $$x^2=6x$$
This statement is sufficient to tell us that x is +ve

(2) $$x=|y|$$, where y is an integer
|y|= + y = x= x is a positive integer
sufficient

D
Intern
Joined: 28 Aug 2016
Posts: 1
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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12 Sep 2018, 16:40
Hi Chetan, in my Evaluation E should be the answer. Could you please specify if my evaluation is wrong.

Given in question: x-->Integer
x^2>1

Now x^2>1 can be solved further as:-

(x^2-1)>0
(x+1)(x-1)>0
this gives us two possibilities:-

x+1>0 & x-1>0
x>-1 & x>1

So this implies that x = 0,1,2,3,4.....

Statement-1:-
x^2=6x
this can be further simplified to
x^2-6x=0
x(x-6)=0
this gives us two possible answers
x=0 or x=6
hence, x can be positive or Zero.
So, Statement-1 is not sufficient

Statement-2:-
x=IyI (I I-->Modulus)
given that y --> Integer
So, y = -2,-1,0,1,2,......
if y = 0 then x = 0
if y = -2,-1,1,2... then x = 2,1,1,2...
Hence, x can be positive or zero.
So, Statement-2 is not sufficient

Together Statement-1 & 2:-
By combining the two statements also we have two possible scenarios of x
x can be positive or Zero.
Hence, not sufficient.

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If x is an integer and x^2>1, is x a positive integer?  [#permalink]

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12 Sep 2018, 16:58
1
sanket272 wrote:
Hi Chetan, in my Evaluation E should be the answer. Could you please specify if my evaluation is wrong.

Given in question: x-->Integer
x^2>1

Now x^2>1 can be solved further as:-

(x^2-1)>0
(x+1)(x-1)>0
this gives us two possibilities:-

x+1>0 & x-1>0
x>-1 & x>1

So this implies that x = 0,1,2,3,4.....

Statement-1:-
x^2=6x
this can be further simplified to
x^2-6x=0
x(x-6)=0
this gives us two possible answers
x=0 or x=6
hence, x can be positive or Zero.
So, Statement-1 is not sufficient

Statement-2:-
x=IyI (I I-->Modulus)
given that y --> Integer
So, y = -2,-1,0,1,2,......
if y = 0 then x = 0
if y = -2,-1,1,2... then x = 2,1,1,2...
Hence, x can be positive or zero.
So, Statement-2 is not sufficient

Together Statement-1 & 2:-
By combining the two statements also we have two possible scenarios of x
x can be positive or Zero.
Hence, not sufficient.

We are given x^2>1 in the question, so x<-1 or X>1 but X cannot be 0..
If x=0, then x^2=0 but we are given x^2>1

Hence only non zero value is possible...
Each statement gives us a definite answer
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If x is an integer and x^2>1, is x a positive integer?   [#permalink] 12 Sep 2018, 16:58
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