gmat prep -- prime numbers

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gmat prep -- prime numbers

by vinviper1 » Sat Jun 07, 2008 7:42 pm
Thanks!
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by Ian Stewart » Sun Jun 08, 2008 6:11 am
A positive integer is a perfect square only if every exponent in its prime factorization is even (choose any whole number at all, prime factorize it, square it, and you should see why). Neither statement comes close to giving us this information:

1) k is divisible by 2^2. k might be (2^2)*3, or 2^3, or a lot of other numbers which are not perfect squares. Not sufficient.

2) k is divisible by four different primes. k might be 2*3*5*7 (or, again, a lot of other numbers which are not perfect squares). Not sufficient.

Even together, k might be (2^2)*3*5*7 (or a lot of other non-squares), so not sufficient.

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by vinviper1 » Mon Jun 09, 2008 7:34 pm
what do you mean by prime factorize it?

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by Ian Stewart » Tue Jun 10, 2008 3:59 am
vinviper1 wrote:what do you mean by prime factorize it?
Divide into primes. For example:

45 = (3^2)*5
72 = (2^3)*(3^2)
120 = (2^3)*3*5

Prime factorizations are very useful in almost every question about divisibility.