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
The question asks for the
greatest possible value of (1/nx).
Which can be rephrased as:
What is the least possible value of (nx)?
Now x is a prime and nx is both the square of an integer and the cube of an integer, where n is a positive integer.
Thus the question becomes:
What is the smallest positive integer which is both the square of an integer and the cube of an integer?
As x is prime and we have to minimize nx, x should be minimum.
Thus, x must be equal to 2. 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.
So minimum value of nx = 2^6 = 64.
Largest possible value of (1/nx) = 1/64.
The correct answer is C.
