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The question asks for the greatest possible value of (1/nx).kushal.adhia wrote:If x is prime and nx is both the square of an integer and the cube of an integer, where n is a positive integer, what is the greatest possible value of (1/nx)?
A. 1
B. 1/32
C. 1/64
D. 1/81
E. 1/729
How do u even go about solving this???
Kushal
How do u get the 6 in the equation?As nx is simultaneously square of an integer and the cube of an integer, nx must be of the form nx = (a^6)*(b^6)... , where a, b... are primes.
Suppose n is an integer which is simultaneously square of an integer (Say, a) and the cube of an integer (Say, b), then n must be such that, n = a^2 and n = b^3. Thus, a^2 = b^3 => a = b^(3/2) and b = a^(2/3).kushal.adhia wrote:How do u get the 6 in the equation?As nx is simultaneously square of an integer and the cube of an integer, nx must be of the form nx = (a^6)*(b^6)... , where a, b... are primes.
Thanks
Dani@MasterGMAT wrote:
1 is the square and the cube of 1, but remember that x has to be an integer.
A prime number is a positive integer that has exactly two distinct positive factors, 1 and itself. 1 does not have two distinct positive factors -- the only positive factor of 1 is 1 -- so by definition 1 is not prime. The smallest prime number is 2.goyalsau wrote:Dani@MasterGMAT wrote:
1 is the square and the cube of 1, but remember that x has to be an integer.
I think you were suppose to write that x has to be a prime number.
Why 1 is not a prime number ?
AS per the definition of prime number , " Numbers which can not be divisible by any other number ( except them selves )
are all prime numbers.
So why 1 is not prime.
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