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# If the Integer n is greater than 1, is n equat to 2?

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If the Integer n is greater than 1, is n equat to 2? [#permalink]

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02 Jan 2004, 12:58
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Q. If the Integer n is greater than 1, is n equat to 2?

1. n has exactly two +ve factors
2. The difference of any two distinct +ve factors of n is odd

---------------------------
Q is from OG, page 308
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02 Jan 2004, 13:02
Q is not that difficut to solve, I have problems understanding the explanation. I feel Ans is C. But official ans is B. Is this a mistake.

analyzing 2.

consider 8. Two distinct factors are 8 and 1. The diff is 7.
consider 2, then it is 2 and 1, diff is odd. So how come we have Ans B. It is only when we take prime Nos and the diff of their factors odd, we get Ans 2.

Eeither I am getting too good, or too dumb to see the obvious.
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02 Jan 2004, 13:17
dj join the gang of smart people then.

May be bb can put such mistakes in OG in a section for every one to refer to. Trying to make sure that my grammar is corret as I write any thing.

ONLY THE PARANOID SURVIVE.
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02 Jan 2004, 13:20
feeling quite queasy, but I will try to write something...

Quote:
Q. If the Integer n is greater than 1, is n equat to 2?

1. n has exactly two +ve factors
2. The difference of any two distinct +ve factors of n is odd

A) tells us that we have only 2 +ve factors.. means, a prime numbes
B) to prove this we need an even prime number. bet on 2 ...

think, it's quite clear. we need both of these
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10 Jan 2004, 17:36
what is meant by distinct factors ? Does it mean only two factors ?

if N is 10 it has two factors (2,5) and (10,1) difference between these is odd
if N is 2 then it has factors( 1,2) difference between them 1 which is odd

We cannot determine the anything from these two conditions.
If distinctive means just one set of factors then B alone is sufficient.

Opps sorry.
C should be the answer. condition one says it clearly that it has exactly two factors.
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14 Jan 2004, 02:01
bat_car wrote:
Q. If the Integer n is greater than 1, is n equat to 2?

1. n has exactly two +ve factors
2. The difference of any two distinct +ve factors of n is odd

---------------------------
Q is from OG, page 308

B)
1) is any prime number
2) the only way the difference of ANY two distinct +ve factor of n is odd is if there are only two of them. think about it. If there are 3 numbers and the difference between A and B is odd and A and C is odd, then B-C MUST be even. Since N must have 1 as a factor, the only possible number for the second factor is 2.
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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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14 Jan 2004, 10:58
Thanks Akhamai for confirming my doubts on this one. I came across this post in the past and wonder how everyone could say it was C when, as everyone even mentioned it, 2 was the only answer to the second statement. dj said it himself
Quote:
B) to prove this we need an even prime number. bet on 2 ...
B it is
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Best Regards,

Paul

14 Jan 2004, 10:58
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