• Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Distinct factor (help)

This topic has 2 expert replies and 6 member replies
aloha Junior | Next Rank: 30 Posts Default Avatar
Joined
20 Jun 2008
Posted:
15 messages

Distinct factor (help)

Post Sat Oct 11, 2008 12:58 pm
I am revising OG 11 for the second time but first time I didn't have problem with this particular DS question and now I just can't get it. I need help.
Its OG 11 DS # 132.
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 distint positive factors of n is odd.

The solution states statement B. But there are other integers >2 for example:28 is greater than 2 and the difference of any two distinct factor of 28 is odd (since 7-2=5).
Also statement 2 does not state that the 2 distinct factors of n are the only factors of n (which would be true when n=2).
Am I missinng something or what? Please help and explain. Thanks in advance.

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Ian Stewart GMAT Instructor
Joined
02 Jun 2008
Posted:
2285 messages
Followed by:
346 members
Upvotes:
1090
GMAT Score:
780
Post Tue Oct 21, 2008 12:31 pm
k2gopal wrote:
Ian Stewart wrote:
Statement 1 just says "n is prime." So not sufficient.

Statement 2 is more interesting:

Suppose n is even, and n > 2. Well, if n is not equal to 2, and n is even, then 2 is a divisor of n. So n and 2 are even, and therefore n-2 is even. This contradicts what we're told in statement 2, so, if n > 2, n can't be even.
Hi Ian,

the bolded statement imho doesn't make sense. Statement 2 is contradicted ONLY if n and 2 were the only factors. The second stem as aloha rightly pointed out says "the difference of any two distinct positive factors of n is odd. " of the two factors. Given that, for the number 28, "7" and "2" are definitely distinct positive factors.

OG11 is almost never wrong, but I strongly feel that their wording should have been distinct prime factors. But again this would cause a problem because the number 1 is not prime. So I'm a little lost with this sum as well. I still feel C would be the right choice. I have no clue still how B figures.

Could anyone please re-look this question, I haven't found a convincing answer yet anywhere.
You and aloha above are both misinterpreting the second statement. When it says

"the difference of any two distinct positive factors of n is odd"

this does *not* mean:

'the difference between some pair of distinct positive factors of n is odd"

which seems to be the way you have both understood it. Instead it means

"the difference between every pair of distinct positive factors of n is odd".

That is, it means that for *any* two factors you of n that you choose, the difference will *always* be odd.

So what could n be?

* If n is even, and n > 2, then 2 and n are both distinct factors of n, and n-2 is even. So n can't be an even number greater than 2;

* If n is odd, and n > 1, then 1 and n are both distinc factors of n, and n-1 is even. So n can't be an odd number greater than 1.

Since we are told n > 1, that only leaves one possibility: n = 2.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

  • +1 Upvote Post
  • Quote
  • Flag
aloha Junior | Next Rank: 30 Posts Default Avatar
Joined
20 Jun 2008
Posted:
15 messages
Post Tue Oct 21, 2008 1:06 pm
k2gopal wrote:
Ian Stewart wrote:
Statement 1 just says "n is prime." So not sufficient.

Statement 2 is more interesting:

Suppose n is even, and n > 2. Well, if n is not equal to 2, and n is even, then 2 is a divisor of n. So n and 2 are even, and therefore n-2 is even. This contradicts what we're told in statement 2, so, if n > 2, n can't be even.
Hi Ian,

the bolded statement imho doesn't make sense. Statement 2 is
contradicted ONLY if n and 2 were the only factors. The second stem as aloha rightly pointed out says "the difference of any two distinct positive factors of n is odd. " of the two factors. Given that, for the number 28, "7" and "2" are definitely distinct positive factors.

OG11 is almost never wrong, but I strongly feel that their wording should have been distinct prime factors. But again this would cause a problem because the number 1 is not prime. So I'm a little lost with this sum as well. I still feel C would be the right choice. I have no clue still how B figures.

Could anyone please re-look this question, I haven't found a convincing answer yet anywhere.
I was first very confused with this problem but if you think this way (looking at statement 2) ...Its talking about the integer (n) which has certain factors and the difference between those factors has to be odd always. So if you look at the example that I mentioned earlier ...28 the factors of which are 1,2,4,7,14,28. N should fulfill the requrement stated in statement 2 which 28 doesn't...
For example
7-4=3 (satisfies)
7-2=5 (satisfies) but
28-14=14 (doesn't satisfy). So stement 2 is not talking about 28.
According to statemnt 2 n should satisfy the requirement and anly n=2 does satisfy this not any other integer. Hope it helps.

  • +1 Upvote Post
  • Quote
  • Flag
andyd Newbie | Next Rank: 10 Posts Default Avatar
Joined
31 Aug 2008
Posted:
4 messages
Post Mon Jun 01, 2009 4:53 pm
Nevermind - sorry for the bump. It finally made sense

  • +1 Upvote Post
  • Quote
  • Flag
k2gopal Junior | Next Rank: 30 Posts Default Avatar
Joined
30 May 2007
Posted:
21 messages
Post Mon Oct 20, 2008 2:25 pm
Ian Stewart wrote:
Statement 1 just says "n is prime." So not sufficient.

Statement 2 is more interesting:

Suppose n is even, and n > 2. Well, if n is not equal to 2, and n is even, then 2 is a divisor of n. So n and 2 are even, and therefore n-2 is even. This contradicts what we're told in statement 2, so, if n > 2, n can't be even.
Hi Ian,

the bolded statement imho doesn't make sense. Statement 2 is contradicted ONLY if n and 2 were the only factors. The second stem as aloha rightly pointed out says "the difference of any two distinct positive factors of n is odd. " of the two factors. Given that, for the number 28, "7" and "2" are definitely distinct positive factors.

OG11 is almost never wrong, but I strongly feel that their wording should have been distinct prime factors. But again this would cause a problem because the number 1 is not prime. So I'm a little lost with this sum as well. I still feel C would be the right choice. I have no clue still how B figures.

Could anyone please re-look this question, I haven't found a convincing answer yet anywhere.

  • +1 Upvote Post
  • Quote
  • Flag
conomav Junior | Next Rank: 30 Posts Default Avatar
Joined
15 Aug 2008
Posted:
14 messages
Post Fri Oct 17, 2008 5:39 pm
what is difference between distinct positive factor & positive factor

  • +1 Upvote Post
  • Quote
  • Flag
aloha Junior | Next Rank: 30 Posts Default Avatar
Joined
20 Jun 2008
Posted:
15 messages
Post Sun Oct 12, 2008 1:16 pm
parallel_chase wrote:
aloha wrote:
2)the difference of any two distint positive factors of n is odd.
advance.
This statement actually means that difference between any two factors of n out of all the factors of n is odd

if n= 28
factors of n = 1,2,4,7,14,28
4-2 = 2 even
14-4 = 10 even
28-14 = 14 even

Therefore, if we follow the above statement n can never be 28.

it is best to try with prime integers because if we try with odd non prime integers, factors can be two odd numbers, the difference of two odd factors is even, and same goes with even non prime integers, difference of any two even integers is also even integer.

every odd prime integer will give us the difference of even number.
therefore only one situation fits the criteria i.e. if n=2, factor: 1, 2
2-1 = 1

Hope this helps.
Thanks a bunch for your reply. One think I want to mention...
If we look at #2 the information we have are: n>1 and the difference of any 2 positive factors of n is odd. So if we use the same example of "28" it is also true that two of the 6 factors of 28 are 7 and 2 and the difference between these two is odd. Again, difference between 7 and 4 is also odd .So n is not necessarily 2. I thought we can be sure about that only if we use both the statements. I am really sorry but am I still missing some thing?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Ian Stewart GMAT Instructor
Joined
02 Jun 2008
Posted:
2285 messages
Followed by:
346 members
Upvotes:
1090
GMAT Score:
780
Post Sat Oct 11, 2008 4:04 pm
aloha wrote:
I am revising OG 11 for the second time but first time I didn't have problem with this particular DS question and now I just can't get it. I need help.
Its OG 11 DS # 132.
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 distint positive factors of n is odd.

The solution states statement B. But there are other integers >2 for example:28 is greater than 2 and the difference of any two distinct factor of 28 is odd (since 7-2=5).
Also statement 2 does not state that the 2 distinct factors of n are the only factors of n (which would be true when n=2).
Am I missinng something or what? Please help and explain. Thanks in advance.
Statement 1 just says "n is prime." So not sufficient.

Statement 2 is more interesting:

Suppose n is even, and n > 2. Well, if n is not equal to 2, and n is even, then 2 is a divisor of n. So n and 2 are even, and therefore n-2 is even. This contradicts what we're told in statement 2, so, if n > 2, n can't be even.

Okay, suppose n is odd. Well, then 1 is a factor of n, and since n is a factor of n, n-1 must be even (since odd-odd = even). But this contradicts what we're told in Statement 2. So n can't be odd.

There's only one possibility we haven't considered yet: n = 2. All other cases are impossible, so n must be equal to 2, and statement 2 is sufficient.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

  • +1 Upvote Post
  • Quote
  • Flag
parallel_chase Legendary Member Default Avatar
Joined
20 Jun 2007
Posted:
1153 messages
Followed by:
2 members
Upvotes:
146
Target GMAT Score:
V50
Post Sat Oct 11, 2008 2:08 pm
aloha wrote:
2)the difference of any two distint positive factors of n is odd.
advance.
This statement actually means that difference between any two factors of n out of all the factors of n is odd

if n= 28
factors of n = 1,2,4,7,14,28
4-2 = 2 even
14-4 = 10 even
28-14 = 14 even

Therefore, if we follow the above statement n can never be 28.

it is best to try with prime integers because if we try with odd non prime integers, factors can be two odd numbers, the difference of two odd factors is even, and same goes with even non prime integers, difference of any two even integers is also even integer.

every odd prime integer will give us the difference of even number.
therefore only one situation fits the criteria i.e. if n=2, factor: 1, 2
2-1 = 1

Hope this helps.

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 161 topics
2 lheiannie07 110 topics
3 ardz24 56 topics
4 LUANDATO 53 topics
5 Vincen 50 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

151 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

145 posts
3 image description GMATGuruNY

The Princeton Review Teacher

114 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
5 image description Scott@TargetTestPrep

Target Test Prep

98 posts
See More Top Beat The GMAT Experts