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

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If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 05:11
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Difficulty:

65% (hard)

Question Stats:

46% (00:42) correct 54% (00:58) wrong based on 70 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-the-integ ... 94720.html
[Reveal] Spoiler: OA

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 05:22
DeepGagan wrote:
if n > 1, is n=2?

(1) n has exactly 2 positive factors.

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

(1) is ins. Consider 3, 5, 7 -- any primes
(2) to have the difference of any two distinct factors odd, these factors must be even and odd simultaneously.
odd-even=odd
even-odd=odd

The only number that has such factors is 2.
(B)

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 06:13
DeepGagan wrote:
if n > 1, is n=2?

(1) n has exactly 2 positive factors.

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

stmnt 1: n could be 2, 3 5 or 7. not sufficient

stmnt 2: has to be 2. 2 has only 2 factors (2,1) whose diff is 2. try this with some other nos and this stment wont hold.

B.

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 08:08

statement 1: Any prime number has two positive factors so INSUFFICIENT.

statement 2: Only when n = 2, you can have its factors subtract to an odd number (1). Sufficient.
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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 11:02
guys not sure if i understood the question correctly, but can n be 12,18, 20 etc

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 11:55
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Sudhanshuacharya wrote:
guys not sure if i understood the question correctly, but can n be 12,18, 20 etc

No. I assume you are referring to stment 2.

Lets take 12- factors are 1,2,3,4,6 and 12. Diff b/w any 2 factors should be odd, which is not the case with 12. Only 2 fulfills this condition.

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 12:02
Chetangupta wrote:
Sudhanshuacharya wrote:
guys not sure if i understood the question correctly, but can n be 12,18, 20 etc

No. I assume you are referring to stment 2.

Lets take 12- factors are 1,2,3,4,6 and 12. Diff b/w any 2 factors should be odd, which is not the case with 12. Only 2 fulfills this condition.

Ok. I guess i had missed part "any 2 factors" from the statement. Thanks for your clarification

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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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21 Jul 2011, 12:37
Sudhanshucharya - Same issue with me - this clears it up for me.
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Re: If the integer n is greater than 1, is n equal to 2? [#permalink]

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05 Dec 2017, 23:53
If the integer n is greater than 1, is n equal to 2?

(1) Any prime satisfies this statement (2, 3, 5, ...), thus n may or may not equal to 2. Not sufficient.

(2) n has at least following factors: 1 and n (the number itself). As given that "the difference of any two distinct positive factors of n is odd", then must be true that: $$n-1=odd$$ --> $$n=odd+1=even$$. Can $$n$$ be even number more than 2? No, because if $$n=even>2$$ it obviously has 2 as a factor and again as "the difference of any two distinct positive factors of n is odd", then n-2 must be odd, but $$n-2=even-2=even\neq{odd}$$. Hence $$n=2$$. Sufficient.

OR: "the difference of any two distinct positive factors of n is odd" means that number must have only one odd factor and only one even factor. (If odd factors, (or even factors) >1, then the difference of the pair of two odd factors (or even factors) will be even not odd). Only number to have only one odd and only one even factor is 2. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-the-integ ... 94720.html
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Re: If the integer n is greater than 1, is n equal to 2?   [#permalink] 05 Dec 2017, 23:53
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