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If x2 is a positive integer, is x a positive integer?

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If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 15 Sep 2018, 19:38
1
6
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

21% (01:00) correct 79% (01:16) wrong based on 111 sessions

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If \(x^2\) is a positive integer, is \(x\) a positive integer?


(1) \(\sqrt{x^2}\) is an integer.

(2) \(\sqrt{x^2} = x\)

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Re: If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 15 Sep 2018, 21:30
3
If \(x^2\) is a positive integer, is \(x\) a positive integer?
\(x/\neq{0}\)

(1) \(\sqrt{x^2}\)is an integer.
If x is -3, \(\sqrt{(-3)^2}\)=3
Same if x is 3..
Insufficient

(2) \(\sqrt{x^2}\) = \(x\)
x>0
Say \(x^2=3........\sqrt{x^2}=\sqrt{3}.......x=√3\)...x is positive but not integer
But x=3....xis positive and integer
Insufficient

Combined..
x>0...
And if x>0, then √(x^2) can be integer only when x is integer..
So x is positive and also integer
Sufficient

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Re: If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 16 Sep 2018, 10:13
(1) \(\sqrt{x^2}\) is an integer. --> x is an integer. But we don't know whether x is positive or negative. --> Not sufficient.
Number plugging:
If \(\sqrt{3^2}= 3\) --> \(x=3\) --> Yes.
If \(\sqrt{(-3)^2}= 3\) --> \(x=-3\) --> No.

(2) \(\sqrt{x^2} = x\) --> x is positive. But we don't know whether x is integer. --> Not sufficient.
Number plugging:
If \(\sqrt{3^2}= 3\) --> \(x=3\) --> Yes.
If \(\sqrt[]{(\sqrt[]{3})^{2}} = \sqrt[]{3}\) --> \(x=\sqrt[]{3}\) --> No.

(1) + (2): x is an integer AND x is positive.--> Yes --> Sufficient.

Answer C.

Harshgmat wrote:
If \(x^2\) is a positive integer, is \(x\) a positive integer?


(1) \(\sqrt{x^2}\) is an integer.

(2) \(\sqrt{x^2} = x\)

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If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 10 Dec 2018, 02:56
In statement (2) ,

why can't X be negative?
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Re: If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 10 Dec 2018, 03:04
LHS is square root of a real number => LHS is not negative.

Hope it's clear.

Pritam_Pf wrote:
In statement (2) ,

why can't X be negative?

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Re: If x2 is a positive integer, is x a positive integer?  [#permalink]

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New post 10 Dec 2018, 03:42
x^2 has to be +ve as it's under square root. This does not mean that x has to be +ve.x canbe -ve.

So correct answer should be E.

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Re: If x2 is a positive integer, is x a positive integer?   [#permalink] 10 Dec 2018, 03:42
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