Problem Solving

sanju09 wrote:If S is the set of all factors of a perfect square integer N, which of the following is NOT true?
A. Set S contains an odd number of elements.
B. Median of set S is the square root of N.
C. N cannot equal 0 in order to define S.
D. N cannot equal 1 in order to define S.
E. Sum of all elements of set S is a prime number.


MBM

This question doesn't seem to make any sense. D certainly is not true; we can easily define the set of positive factors (I'm assuming you mean the word 'positive' to appear in the question) of 1 - we get the set {1}. C is not true either; we can define S to be the set of all positive divisors of zero (zero is divisible by every positive integer, so that will just be the infinite set consisting of all positive integers). The median of the set will be the square root of n if n is positive, but not if n is zero, so B might be true, and might not. The number of elements in S will be odd if n is positive, but will be infinite if n is zero, so A might be true, and might not. E is sometimes true, sometimes not; if n=1 or n=7 it is not true, and if n=2 or n=3 it is true.