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Is n the square of an integer?
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
Nightfury14
Joined: 13 Sep 2015
Last visit: 02 May 2023
Posts: 124
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Schools: ISB '20 INSEAD Jan '19
23 Jan 2017, 10:01
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Bunuel
Is n the square of an integer?
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
Statement 1)
n could be the square root of 4 => n=2 (n is not the square of an integer)
n could be the square root of 16 => n=4 (n is the square of an integer)
Not sufficient
Statement 2)
\(\sqrt{9n}\) translates to \(3\sqrt{n}\) => this expression could be square of an integer if n is
1. n=9 or \(3^2\) => \(3\sqrt{9}\) => 3*3 n is square of an integer.
2. n=9*9*9 or \(27^2\)=> \(3\sqrt{9*9*9}\) =>9*9 n is square of an integer.
Note n cannot be 9*9 as then the resultant expression would not be a square itself as defined by statement 2.
Sufficient
Ans. B
23 Jan 2017, 11:46
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Nightfury14
Bunuel
Is n the square of an integer?
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
(1) n is the square root of an integer
(2) \(\sqrt{9n}\) is square of an integer
Statement 1)
n could be the square root of 4 => n=2 (n is not the square of an integer)
n could be the square root of 16 => n=4 (n is the square of an integer)
Not sufficient
Statement 2)
\(\sqrt{9n}\) translates to \(3\sqrt{n}\) => this expression could be square of an integer if n is
1. n=9 or \(3^2\) => \(3\sqrt{9}\) => 3*3 n is square of an integer.
2. n=9*9*9 or \(27^2\)=> \(3\sqrt{9*9*9}\) =>9*9 n is square of an integer.
Note n cannot be 9*9 as then the resultant expression would not be a square itself as defined by statement 2.
Sufficient
Ans. B
Nightfury14
what if n =1/9 ??
