Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

(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.

Does two distinct factors mean that there are only two factors? If not, n can equal 20...5 and 4... 5-4=1. 1 is odd....

Oh..is it because if n=20, then 10 and 2 (which are also factors of 20) -- 10-2=8...even... not odd..

So does (2) mean that all factors of n that are different from each other, when subtracted, must be odd?

I don't have a solid understanding of the laws that would make this more concrete.

Statement (2): "the difference of ANY two distinct positive factors of n is odd", which means that when we pick ANY two distinct factors of n their difference must be odd.

So for n=20. Factors of n are: 1, 2, 4, 5, 10 and 20. 20-1=odd but 20-10=even, so n could not be 20.

Again: "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.

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.

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

Bunuel, I have a doubt regarding statement 1. Can \(\sqrt{2}\) be a factor here? If so then statement 1 is sufficient to say that \(n\) is not equal to \(2\), because \(2\) has factors \(1, \sqrt{2}\) and \(2\).
_________________

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.

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

Bunuel, I have a doubt regarding statement 1. Can \(\sqrt{2}\) be a factor here? If so then statement 1 is sufficient to say that \(n\) is not equal to \(2\), because \(2\) has factors \(1, \sqrt{2}\) and \(2\).

Factor of an integer \(n\), is an integer which evenly divides \(n\) without leaving a remainder.

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

Show Tags

31 Jan 2012, 10:34

1

This post received KUDOS

1

This post was BOOKMARKED

+1 B

Let's analyze statement (2): The difference of any two distinct positive factors of n is odd. Thisn means that any pair of factors of n is compound by an even number and an odd number. This also means that n is a prime number. Why? Because if n had more than two factors, the difference of at least one pair of factors would be even. For example, if there were an additional odd number, there would be a pair of numbers whose difference would be even. So, if n is a prime number whose has an odd factor and a even factor, then we are talking about the number 2.

ANSWER: B

I think I deserve kudos
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

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

Show Tags

17 Mar 2012, 05:39

Hello Bunuel, Following the last post, I have the same doubt. Basically, if for example if I take number n = 6, then its two distinct factors 3 and 2 or factors 6 and 1 has the difference as odd... so n not equal to 2... can you please explain where am I wrong?

Hello Bunuel, Following the last post, I have the same doubt. Basically, if for example if I take number n = 6, then its two distinct factors 3 and 2 or factors 6 and 1 has the difference as odd... so n not equal to 2... can you please explain where am I wrong?

The difference of ANY two distinct positive factors of n is odd: if n=6 then 6-2=4=even, hence n cannot be 6, or any other number but 2.

If the integer n is greater than 1, is n equal to 2? (1) n has exactly two positive factors (2) The difference between any two distinct positive factors is odd.

I just have one question related to wording of option (2). Should it mention as two distinct prime factors instead of two distinct positive factors?

If the integer n is greater than 1, is n equal to 2? (1) n has exactly two positive factors (2) The difference between any two distinct positive factors is odd.

I just have one question related to wording of option (2). Should it mention as two distinct prime factors instead of two distinct positive factors?

Please provide answer with explanation.

Merging similar topics. Please ask if anything remains unclear.

P.S. The wording of the second statement is correct.
_________________

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

Show Tags

19 Oct 2012, 23:43

Sir Bunuel, I have a doubt here with regards to strategy:

(1) says : n has exactly two positive factors This means that n is a prime no

(2) says: The difference between any two distinct positive factors is odd.

Now to plug in numbers to check the sufficiency of (2) , I didn't chose non prime numbers because (1) and (2) can never contradict each other. So choosing 6,8 , 10 or any non prime no is basically stupidity. What do you say?

Regards, Sach
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Sir Bunuel, I have a doubt here with regards to strategy:

(1) says : n has exactly two positive factors This means that n is a prime no

(2) says: The difference between any two distinct positive factors is odd.

Now to plug in numbers to check the sufficiency of (2) , I didn't chose non prime numbers because (1) and (2) can never contradict each other. So choosing 6,8 , 10 or any non prime no is basically stupidity. What do you say?

Regards, Sach

Yes, the statements in DS questions never contradict each other but your logic for testing numbers is not correct. Consider example below:

Is n=2?

(1) n is prime (2) n is even

Now, if you test only even primes for the second statement you'll have that n could only be 2, since 2 is the only even prime. Therefore you'll get that (2) is sufficient, which is not.

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

Show Tags

26 Oct 2012, 06:07

Bunuel wrote:

sachindia wrote:

Sir Bunuel, I have a doubt here with regards to strategy:

(1) says : n has exactly two positive factors This means that n is a prime no

(2) says: The difference between any two distinct positive factors is odd.

Now to plug in numbers to check the sufficiency of (2) , I didn't chose non prime numbers because (1) and (2) can never contradict each other. So choosing 6,8 , 10 or any non prime no is basically stupidity. What do you say?

Regards, Sach

Yes, the statements in DS questions never contradict each other but your logic for testing numbers is not correct. Consider example below:

Is n=2?

(1) n is prime (2) n is even

Now, if you test only even primes for the second statement you'll have that n could only be 2, since 2 is the only even prime. Therefore you'll get that (2) is sufficient, which is not.

Hope it's clear.

Its not clear. From what I understand So if the 2 statements don;t contradict each other, I shuold still test numbers considering B as an individual statement without have any bearing of A. Please confirm if my understnading is right.
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

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

Show Tags

26 Feb 2013, 05:29

1

This post received KUDOS

dimitri92 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.

From F.S 1, we have that n has only two positive factors. Including the number itself and 1, this can only be a prime. Thus not sufficient as n can be any prime number.

From F.S 2, we have that the difference of any two positive factors is odd. We know that odd-even/even-odd = odd. So we know that "n" has at-least 2 factors , one of which is odd and one is even. Now we don't know whether this integer has only two factors. Say it has 3 factors. The third factor will either be odd or even. Now the presence of the statement any two distinct positive factors makes it essential that any two factors when subtracted give an odd integer. This will not be possible if we have any more factors than an odd factor and an even factor. Thus the number can only have only two factors, one odd and one even. This means the integer can only be 2. Thus, sufficient.

Its not clear. From what I understand So if the 2 statements don;t contradict each other, I shuold still test numbers considering B as an individual statement without have any bearing of A. Please confirm if my understnading is right.

Yes. The two statements cannot contradict each other. But when analyzing one statement, you should as good as forget the previous one. (In some cases, one statement can give you an idea of what numbers you should try and hence be helpful but you will need to try others as well)

Take a simple example:

Is n divisible by 6?

1. n is even 2. n is a multiple of 3

When you try out statement 1, say, you try out 3 numbers: 2, 4, 6. You say 2 and 4 are not divisible by 6 but 6 is. So not sufficient.

When you try out statement 2, will you try only even multiples of 3? No. You will try all multiples of 3. 3 is not divisible by 6 but 6 is. Not sufficient. If you try only even multiples of 3, you will see that all even multiples of 3 are divisible by 6. So your answer will be 'sufficient'. But mind you, here you have used both statements together hence you will mark (C). So in essence, you did not analyze statement 2 alone at all. Answer could have been (B), we will never know (in the actual test!).

Hence, when analyzing each statement, do not look at the data of the other one. In fact, as far as possible, I try to re-read the question stem between the two statements to remind me of exactly what I have to consider and to help me forget the data I have already considered (else you might use it sub-consciously) Sometimes, one statement helps you cheat by giving you ideas of numbers you should try in addition to others, that's all.
_________________

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.

(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.

Answer: B.

Maybe a silly doubt...When you say a number has 2 factors or 4 factors..is 1 also included in it?I usually exclude 1 when counting factors..pls cllarify..

gmatclubot

Re: is n equal to 2?
[#permalink]
10 Sep 2013, 03:15

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Term 1 has begun. If you're confused, wondering what my post on the last 2 official weeks was, that was pre-term. What that means is that the school...