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# ds question

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Intern
Joined: 11 Sep 2006
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05 Oct 2006, 14:08
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Is n an integer?
(1) n^2 is an integer
(2) n^1/2 is an integer.

My answer is D that they are each sufficient. My logic is that if n squared is an integer, then n has to be an integer. When is there an instance that n squared is an integer but n isnt.

Can someone explain this to me.

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SVP
Joined: 01 May 2006
Posts: 1794

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05 Oct 2006, 14:12
Pick numbers

Stat 1 :
o n^2 = 4 > n = 2 or n = -2
o n^2 = 5 > n = sqrt(5) or n = -sqrt(5)

INSUFF

Stat 2 :
sqrt(n) = k (k an integer)
<=> n = k^2 = k*k
Thus, n is an integer

SUFF

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SVP
Joined: 05 Jul 2006
Posts: 1742

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05 Oct 2006, 14:25
Is n an integer?
(1) n^2 is an integer
(2) n^1/2 is an integer.

ONE

N COULD BE SQRT OF AN INTIGER..........NOT SUFF

FROM TWO

SQRT N IS INTIGER THUS SURE N IS INTIGER..SUFF

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Director
Joined: 06 Sep 2006
Posts: 736

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05 Oct 2006, 14:55
Is n an integer?
(1) n^2 is an integer
(2) n^1/2 is an integer.

1) arbitrary values for n^2=0,1,2,3,4,.. so we can't sat if n is an integer INSUFF.

2) n^1/2 = 1, 2, 3, 4, 5
picking any and squaring both sides will leave us with an integer.
SUFFICIENT

B.

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Senior Manager
Joined: 30 Aug 2006
Posts: 374

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05 Oct 2006, 16:15
B

n could be sqrt(2) or sqrt(3) or sqrt(7) etc.

sqrt(7) * sqrt(7) = 7, but sqrt(7) is not an integer.

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05 Oct 2006, 16:15
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