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.
DS - Is n an integer ?
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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
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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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
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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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 !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
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?
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?