500 ds test4#17

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dunkin77
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Topic: 500 ds test4#17

Thu Apr 05, 2007 5:38 pm

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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
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Fri Apr 06, 2007 11:23 am

dunkin77 wrote: 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 2^23^2... 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 .. 2^33^2 ... 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 ...