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OG - DS - #132, #128

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anish
 Post subject: OG - DS - #132, #128
 Post Posted: Fri Jun 08, 2007 2:14 am 
Pls provide the soln for the following with explaination


132) If the integer n is greater than 1, is n equal to 2

1) n has exactly 2 positive factors

2) The difference of any two distinct positive factors of n is odd.


128. If X is an integer is X |X| < 2 x

1)X < 0

2)X=10
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dbernst
 Post subject:
 Post Posted: Sat Jun 09, 2007 12:51 am 
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ManhattanGMAT Staff


Posts: 304
Anish,

We cannot comment on problems unless we know their source. Please cite your problems, and we will be glad to assist you.

Thanks!
-dan
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Guest
 Post subject:
 Post Posted: Sun Jun 10, 2007 10:50 pm 
OG 11
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Anish
 Post subject:
 Post Posted: Sun Jun 10, 2007 10:51 pm 
Source is OG 11
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GMATPaduan
 Post subject:
 Post Posted: Tue Jun 12, 2007 3:51 pm 
132.

n>1, is n = 2?
(1) n is prime
Not Sufficient - n could be 2 or any other prime number

(2) The difference of any two distinct positive factors of n is odd.
Sufficient - This is only true of the prime number 2

* If n is a prime other than two, the difference of its two positive factors will be even (1 and itself) --
Odd - Odd = Even

* If n is an even non-prime number, then it will have some difference in factors that are odd (1 and the even number - Even - Odd = Odd), and then it will be divisible by an even number (2 at a minimum) - and the difference between even and even is Even

* if n is an odd non-prime number (15), then it will have some difference in factors that are Even (15 -1); but it will also have two odd factors if it is not prime - given that odd * odd = odd, and Odd - Odd = Even (so B is sufficient)
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