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If K is a positive integer...

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michael.thorsen
 Post subject: If K is a positive integer...
 Post Posted: Thu May 20, 2010 3:33 pm 
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Course Students


Posts: 2
If K is a positive integer, is K the square of an integer?
1)K is divisible by 4
2)K is divisible by exactly four different prime numbers

OA=E

I was confused by statement 2. Four different prime numbers-does that mean four total (and different) as in [2,3,5,7] or can that mean [2,2,3,3,5,5,7,7]
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RonPurewal
 Post subject: Re: If K is a positive integer...
 Post Posted: Sun May 23, 2010 6:28 am 
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ManhattanGMAT Staff


Posts: 6765
michael.thorsen wrote:
If K is a positive integer, is K the square of an integer?
1)K is divisible by 4
2)K is divisible by exactly four different prime numbers

OA=E

Quote:
I was confused by statement 2. Four different prime numbers-does that mean four total (and different) as in [2,3,5,7] or can that mean [2,2,3,3,5,5,7,7]


it means the latter.
(statements about divisibility do not determine how many times a given factor will go into a number; they only determine whether that factor will go into the number.)

--

notice that you can actually figure this out, if you recall that the two statements never contradict each other on a data sufficiency problem.

specifically, note that statement (1) requires the presence of TWO "2"s in the prime factorization of k. since this statement is not allowed to contradict statement (2), your first possible interpretation above is ruled out.
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s.aamershah
 Post subject: Re: If K is a positive integer...
 Post Posted: Sat May 29, 2010 6:01 pm 
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Students


Posts: 20
I want to make sure I understand the answer. Because b) can mean k= (2,2,3,3,5,5,7,7) and this also satisfies a) the resulting answer is a perfect square because all the prime factors are in pairs and the answer to the question is "k the square of an integer" is yes

BUT b) can also mean k= (2,2,2,3,3,3,5,5,5,7,7,7) in which case this still satisfies a) but this is actually a perfect cube since all the factors are in groups of three and in this case the answer the to the question is "k the square of an integer" is no.

Is this why the answer is E) ?
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mschwrtz
 Post subject: Re: If K is a positive integer...
 Post Posted: Sat Jun 12, 2010 1:10 am 
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ManhattanGMAT Staff


Posts: 506
yes, well-put.
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