500 ds test4#17

[dunkin77]

Hi,

The answer is B) but I need explanation....please help!


. Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p^2.
(2) root n is an integer

[gabriel]

Hi,

The answer is B) but I need explanation....please help!


. Is the positive integer n equal to the square of an integer?
(1) For every prime number p, if p is a divisor of n, then so is p^2.
(2) root n is an integer

well B is pretty obvious .. if root of n is ann integer that is bcoz n is the square of another intger ..

let me focus on A .. consider a number 2^2*3^2... so the prime numbers that divide n are 2,3 and as the statement says both 2^2 and 3^2 are also factors of n .. in this case n is a square of an integer ...

now consider another number .. 2^3*3^2 ... in this case too the prime factors are 2,3 and also 4 and 9 divide the number but the number is not the square of an integer .. so A does not give a defnite answer .. so is insufficient ...