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If x is an integer and x^2>1, is x a positive integer?
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02 Sep 2018, 07:51
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63% (01:01) correct 37% (01:09) wrong based on 142 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!!...
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: If x is an integer and x^2>1, is x a positive integer?
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02 Sep 2018, 07:58
From statement 1: X^26X = 0 X(X6) = 0 X = 0 or 6. Since X^2>0 then X = 6. 1 is sufficient. From statement 2: X = +Y or Y. No info about Y. Hence insufficient. A is the answer Posted from my mobile device
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Joined: 13 Jun 2017
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Re: If x is an integer and x^2>1, is x a positive integer?
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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.
D is the answer



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Re: If x is an integer and x^2>1, is x a positive integer?
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02 Sep 2018, 09:36
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, \(x^26x=0\) Or, x(x6)=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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Re: If x is an integer and x^2>1, is x a positive integer?
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02 Sep 2018, 13:46
[quote="Afc0892"]From statement 1:
X^26X = 0 X(X6) = 0 X = 0 or 6.
Since X^2>0 then X = 6. 1 is sufficient.
From statement 2: X = +Y or Y.
No info about Y. Hence insufficient.
A is the answer.
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.



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Re: If x is an integer and x^2>1, is x a positive integer?
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03 Sep 2018, 02:42
selim wrote: Afc0892 wrote: From statement 1:
X^26X = 0 X(X6) = 0 X = 0 or 6.
Since X^2>0 then X = 6. 1 is sufficient.
From statement 2: X = +Y or Y.
No info about Y. Hence insufficient.
A is the answer.
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?



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



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Re: If x is an integer and x^2>1, is x a positive integer?
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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^21)>0 (x+1)(x1)>0 this gives us two possibilities:
x+1>0 & x1>0 x>1 & x>1
So this implies that x = 0,1,2,3,4.....
Statement1: x^2=6x this can be further simplified to x^26x=0 x(x6)=0 this gives us two possible answers x=0 or x=6 hence, x can be positive or Zero. So, Statement1 is not sufficient
Statement2: 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, Statement2 is not sufficient
Together Statement1 & 2: By combining the two statements also we have two possible scenarios of x x can be positive or Zero. Hence, not sufficient.
So Answer: E



Math Expert
Joined: 02 Aug 2009
Posts: 7037

Re: If x is an integer and x^2>1, is x a positive integer?
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12 Sep 2018, 16:58
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^21)>0 (x+1)(x1)>0 this gives us two possibilities:
x+1>0 & x1>0 x>1 & x>1
So this implies that x = 0,1,2,3,4.....
Statement1: x^2=6x this can be further simplified to x^26x=0 x(x6)=0 this gives us two possible answers x=0 or x=6 hence, x can be positive or Zero. So, Statement1 is not sufficient
Statement2: 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, Statement2 is not sufficient
Together Statement1 & 2: By combining the two statements also we have two possible scenarios of x x can be positive or Zero. Hence, not sufficient.
So Answer: E 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
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: If x is an integer and x^2>1, is x a positive integer? &nbs
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