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square integer N

by sanju09 » Tue Apr 21, 2009 5:51 am
If S is a finite 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.


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Last edited by sanju09 on Wed Apr 22, 2009 1:23 am, edited 1 time in total.
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Re: square integer N

by Ian Stewart » Tue Apr 21, 2009 8:02 am
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.
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by sanju09 » Wed Apr 22, 2009 1:33 am
Thanks Ian for paying a careful glance at it. Your suggestions have made me make only one change in the wordings of the question presented.

A perfect square integer cannot be negative, this I believe; where am I wrong there? I request you to see through the single change (i.e. S is a finite set) and the choice E once, and let us know if it could now make any sense. Thanks B-)
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