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DS - Is n an integer ?

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by II » Sun Aug 10, 2008 2:58 pm
Is n an integer ?

(1) n² is an integer

(2) √n is an integer

I am interested in learning different approaches in solving this particular question. Thanks.
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by raunekk » Sun Aug 10, 2008 3:24 pm
can it be done other then pluggin numbers?

N^2=2 , then N is not an integer.
N^2=4 , N is an integer.
1- insuff

Sq root N is an integer.

Then N definately will be an integer.

2-suff

Hence,B
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by pepeprepa » Sun Aug 10, 2008 3:41 pm
1) is insufficient it's ok

2)
sqrt(n) is an integer
The possible values of n so as sqrt(n) is an integer are 1 4 9 16 25 36 ...
n has to be the square of a number so n has to ba an integer

Hope it helps
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by II » Mon Aug 11, 2008 12:32 am
Guys ... I suppose I am looking for a more thoery based answer to this, rather than just plugging in numbers ...
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by pepeprepa » Mon Aug 11, 2008 3:02 am
Between plugging in and theory, I would opt for plugging in most of the time...

For the 1)
n^2 is an integer --> counter-example with n=sqrt(2)

For the 2)
sqrt(n) is an integer --> The form of "n" is: n=a^2 with "a" an integer --> The square of an integer is an integer --> n is an integer
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by II » Mon Aug 11, 2008 1:36 pm
pepeprepa wrote:Between plugging in and theory, I would opt for plugging in most of the time...

For the 1)
n^2 is an integer --> counter-example with n=sqrt(2)

For the 2)
sqrt(n) is an integer --> The form of "n" is: n=a^2 with "a" an integer --> The square of an integer is an integer --> n is an integer
Thanks pepeprepa ... I agree that in a lot of the cases plugging numbers is more efficient, but I want to make sure I understand the theory behind these things !
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by cholloway » Mon Jul 13, 2009 4:37 pm
I seem to be missing something. What number can you square to get two? Wouldn't that just be an approximation?
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by shibal » Mon Jul 13, 2009 5:05 pm
cholloway wrote:I seem to be missing something. What number can you square to get two? Wouldn't that just be an approximation?
1,4142135623731
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by cholloway » Mon Jul 13, 2009 5:09 pm
From Wikipideia - The square root of 2, also known as Pythagoras' constant, is the positive real number that, when multiplied by itself, gives the number 2.

Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value truncated to 65 decimal places[1] is:

1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799....


I thought gmat only deals with rational numbers?
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