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

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If the integer n is greater than 1, is n equal to 2? (1) n [#permalink] New post 07 Mar 2006, 17:24
00:00
A
B
C
D
E

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

(1) n has exactly two positive factors
(2) The difference of any two distinct positive
factors of n is odd

Apologies if this has been posted already. I dont quite understand the official explanation. I want see your explanations

Thanks
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 [#permalink] New post 07 Mar 2006, 17:40
St 1:

Any prime number will have two +ve factor.

INSUFFICIENT.

St2:

This is also not sufficient because there could be any number of factors.

Combining these two.

for prime number 2.
difference of two factors is one.

Hence YES.

Ans is C
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 [#permalink] New post 07 Mar 2006, 17:51
My reasoning was also similar

All prime numbers have two factors (the number itself and 1)

so (1) is NOT SUFFICIENT


in case of (2)

if you take 16, which is greater than 1
whose factors are 1, 2, 4, 8, 16
difference of any two distinct factors could be odd or even

in case of 9, the difference any two distinct factors is even only

NOT SUFFICIENT

but combining 2 is the only one which has exactly two factors and the difference of the factors as odd

but the official answer is ... different
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Re: DS 132 [#permalink] New post 07 Mar 2006, 18:16
If the integer n is greater than 1, is n equal to 2?

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

--------------------------------------------------------------------------
I guess the statement (1) is a trap. We don't need statement (1). Statement (2) alone is sufficient.

(2) 2 is the only number which satisfies the condition stated in the statement (2).

All the odd numbers has at least two odd positive factors (1 and itself), and thus the difference of these two factors is even.
All the even numbers except 2 has at least two even positive factors (2 and itself) and thus the difference of these two factors is even.

Therefore, 2 is the only number which satisfies the statement (2).
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 [#permalink] New post 07 Mar 2006, 18:23
Taking example 12 (>1)

I thougt 1, 2, 3, 4, 6 & 12 are the factors of 12

If that's correct then the DIFFERENCE of ANY two DISTINCT factors are

say,

1 & 4 which is ODD

2 & 6 which is EVEN

isn't?
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 [#permalink] New post 07 Mar 2006, 19:44
gmatkrishna wrote:
Taking example 12 (>1)

I thougt 1, 2, 3, 4, 6 & 12 are the factors of 12

If that's correct then the DIFFERENCE of ANY two DISTINCT factors are

say,

1 & 4 which is ODD

2 & 6 which is EVEN

isn't?


Yes, it is correct. The differences of any two factors of 12 can be odd or even, depending on which two factors you select. That's why the number 12 does not satisfy the statement (2).

For every number except for 2, the differences of any two factors can be odd or even.

Thus, statement 2 alone is sufficient.
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 [#permalink] New post 07 Mar 2006, 20:11
Got it!

It was because of hard wired thinking on my part when dealing with DS questions
when it comes to 'yes' or 'no' questions I always somehow get into a thinking of 'if there is more than one possibility it's insufficient'

mea culpa

Many thanks for the explanations
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Re: DS 132 [#permalink] New post 08 Mar 2006, 18:02
gmatkrishna wrote:
If the integer n is greater than 1, is n equal to 2?
(1) n has exactly two positive factors
(2) The difference of any two distinct positive factors of n is odd


B. only 2 has 2 +ve factors and the difference of these factors is odd (1). 3 has also 2 +ve factors but the diff = 2 - even.
Re: DS 132   [#permalink] 08 Mar 2006, 18:02
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