Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 07:39

GMAT Club Daily Prep

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Does the integer k have at least three different positive

Author Message
TAGS:

Hide Tags

SVP
Joined: 29 Aug 2007
Posts: 2476
Followers: 70

Kudos [?]: 774 [0], given: 19

Re: interger K gmat Official guide [#permalink]

Show Tags

01 Sep 2009, 21:21
bhanushalinikhil wrote:
GMAT TIGER wrote:
bandit wrote:
Q. Does the integer K have at least three different positive prime factors?

1. K/15 is an integer
2. K/10 is an integer

Will post OA after some time.

C cannot be it.
It should be E because K could be 0 or 30 or any multiple of 30.

But the question is "Does the integer K has at least three different positive prime factors?". And the answer is "Yes".
0 - infinitely number of factors.
30 - 2*3*5 (3 factors).

Am I right, GT or am I missing something here?

Not sure.

0 is divisible by any integer/number but not sure whether all numbers are factor of 0.

As said above, the question should clearly say whether K is +ve, -ve or 0 integer.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 22 Jul 2009
Posts: 191
Followers: 4

Kudos [?]: 267 [0], given: 18

Re: interger K gmat Official guide [#permalink]

Show Tags

01 Sep 2009, 22:22
GMAT TIGER wrote:
0 is divisible by any integer/number but not sure whether all numbers are factor of 0.

"0 is divisible by any integer" = "any integer is a factor of 0"

That's just saying the same with different words.

All real numbers are factors of 0.

Here's the wiki entry for zero: http://en.wikipedia.org/wiki/0_(number)
And here the one for factorization, for those brave enough to go into exploring theorems: http://en.wikipedia.org/wiki/Integer_factorization
_________________

Please kudos if my post helps.

SVP
Joined: 29 Aug 2007
Posts: 2476
Followers: 70

Kudos [?]: 774 [0], given: 19

Re: interger K gmat Official guide [#permalink]

Show Tags

01 Sep 2009, 23:06
In Gmat, only factors of +ve integers are considered factors.

powerka wrote:
GMAT TIGER wrote:
0 is divisible by any integer/number but not sure whether all numbers are factor of 0.

"0 is divisible by any integer" = "any integer is a factor of 0"

That's just saying the same with different words.

All real numbers are factors of 0.

Here's the wiki entry for zero: http://en.wikipedia.org/wiki/0_(number)
And here the one for factorization, for those brave enough to go into exploring theorems: http://en.wikipedia.org/wiki/Integer_factorization

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Manager
Joined: 22 Jul 2009
Posts: 191
Followers: 4

Kudos [?]: 267 [0], given: 18

Re: interger K gmat Official guide [#permalink]

Show Tags

01 Sep 2009, 23:35
I've been digging a little deeper into this.

http://en.wikipedia.org/wiki/Fundamenta ... arithmetic ---> According to the Fundamental Theorem of Arithmetic any integer greater than 1 can be written as a unique product of prime numbers.

http://en.wikipedia.org/wiki/Prime_number ----> A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself.

I dare to say that when working with primes one should assume all integers to be positive. It seems that the primality of negative numbers is not really defined. Besides, as pointed by IanStewart above, GMAT divisibility questions are always about positive integers.

Anyway, for those interested in the topic, check the following links:
http://planetmath.org/encyclopedia/Prim ... ation.html
http://www.beatthegmat.com/negative-pri ... t1374.html

Finally, I was partially wrong in my prior post. Yes, it could be argued that if all numbers are factors of 0, all primes are factors of 0. But ... "Many authors assume 0 to be a natural number that has no prime factorization. Thus Theorem 1 of Hardy & Wright (1979) takes the form, "Every positive integer, except 1, is a product of primes,"" (taken from http://en.wikipedia.org/wiki/Fundamenta ... arithmetic) ... so, if not even the math world has decided regarding the prime factorization of 0, better to ignore it too ... GMAT would never ask about something like this.
_________________

Please kudos if my post helps.

Intern
Joined: 22 Sep 2009
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: interger K gmat Official guide [#permalink]

Show Tags

22 Sep 2009, 19:38
I'm sure the word "positive" is misplaced here. The question should read, "Does the positive integer k have at least three prime factors?" this gets rid of the option of having zero as an answer, and "positive prime" is redundant. TYPO!

Posted from my mobile device
Manager
Joined: 25 Mar 2009
Posts: 54
Followers: 1

Kudos [?]: 18 [0], given: 9

Re: interger K gmat Official guide [#permalink]

Show Tags

24 Sep 2009, 09:09
powerka wrote:
I disagree with the previous poster.
k could be 0.
If k=0 then k has "at least three different positive prime factors", as every number is a factor of 0.

Totally agree with Powerka, 0=0*1*3*5*...., so 0 has at least 3 prime factors
Manager
Joined: 22 Sep 2009
Posts: 219
Location: Tokyo, Japan
Followers: 2

Kudos [?]: 22 [0], given: 8

Re: interger K gmat Official guide [#permalink]

Show Tags

22 Nov 2009, 03:19
Not pertaining to this question but I thought the rule was

0 is a multiple for every number and a factor of none.

Is that correct? At least in GMAT
Manager
Joined: 19 Nov 2007
Posts: 222
Followers: 1

Kudos [?]: 277 [0], given: 1

Re: interger K gmat Official guide [#permalink]

Show Tags

22 Nov 2009, 05:27
St1: K=m15, where m is any number; Hence K can have minimum two prime factors (5,3) and let us say that m is prime than three prime factors; Insuff

St2: K=n10, where n is any number; Hence K can have minimum two prime factors (5,2) and let us say that n is prime than three prime factors; Insuff

Combined K can have minimum has to have three prime factors (5,3,2). Hence Suff

Hence C
Manager
Joined: 24 Sep 2009
Posts: 110
Followers: 1

Kudos [?]: 19 [0], given: 2

Re: interger K gmat Official guide [#permalink]

Show Tags

27 Nov 2009, 16:26
I agree with C.
k=2*3*5*i, so at least k has 3 different factors: 2,3,5.
_________________

http://www.online-stopwatch.com/
http://gmatsentencecorrection.blogspot.com/

Intern
Joined: 28 Sep 2009
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: interger K gmat Official guide [#permalink]

Show Tags

13 Jan 2010, 19:50
IanStewart wrote:
If this were a real GMAT question, it would ask "Does the positive integer K have at least three different positive prime factors?" GMAT questions about divisibility are always restricted to positive integers only. That said, zero is not an exception here anyway, as has been pointed out above, but you won't need to worry about that on the real test.

great point by Ian here as I was thrown off by the possibility of K being a negative integer. But now that I know GMAT questions about divisibility are only positive numbers. Thanks for the heads up!
Intern
Joined: 02 Aug 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: interger K gmat Official guide [#permalink]

Show Tags

21 Aug 2010, 09:43
Hey all ,

i think we all are missing another point,

K can be negative as well

Say k=-15

therefore, k/15=-1 which is an integer,

and at the same time k can be +ve;ie k=15

hence my take would be E,
any views...
VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 111

Kudos [?]: 422 [0], given: 73

OG 12 Diagnostic DS Error? [#permalink]

Show Tags

22 Sep 2010, 22:53
I did a search for this topic and didn't find anything, so if this is a repeat question then I apologize.

In the OG 12 diagnostic test I think I found an error in the DS section, question #42.

Does the integer k have at least three different positive prime factors?
(S1) k/15 is an integer
(S2) k/10 is an integer
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Last edited by cheetarah1980 on 22 Sep 2010, 22:55, edited 1 time in total.
VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 111

Kudos [?]: 422 [0], given: 73

Re: OG 12 Diagnostic DS Error? [#permalink]

Show Tags

22 Sep 2010, 22:55
(S1): k is a multiple of 15. If k is 15, prime factors are 3 and 5 (i.e. <3). If k is 30, prime factors are 2,3, and 5 (i.e. =3). If k is 0, there are no prime factors. INSUFFICIENT
(S2): k is multiple of 10. If k is 10, prime factors are 2 and 5 (i.e.<3), if k is 30, once again prime factors=3. If k is 0 there are no prime factors. INSUFFICIENT
Combining S1 and S2: k must be a multiple of both 15 and 10. If k=0, there are no prime factors. If k is any other multiple of both 15 and 10 then prime factors at least include 2,3, and 5 so prime factors are > or = 3. INSUFFICIENT
Therefore the answer should be E

However, OA is C.
Can someone please explain to me where I'm going wrong or am I correct to assume that this is an error.
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Math Expert
Joined: 02 Sep 2009
Posts: 38898
Followers: 7739

Kudos [?]: 106204 [0], given: 11610

Re: OG 12 Diagnostic DS Error? [#permalink]

Show Tags

22 Sep 2010, 23:14
cheetarah1980 wrote:
I did a search for this topic and didn't find anything, so if this is a repeat question then I apologize.

In the OG 12 diagnostic test I think I found an error in the DS section, question #42.

Does the integer k have at least three different positive prime factors?
(S1) k/15 is an integer
(S2) k/10 is an integer

cheetarah1980 wrote:
(S1): k is a multiple of 15. If k is 15, prime factors are 3 and 5 (i.e. <3). If k is 30, prime factors are 2,3, and 5 (i.e. =3). If k is 0, there are no prime factors. INSUFFICIENT
(S2): k is multiple of 10. If k is 10, prime factors are 2 and 5 (i.e.<3), if k is 30, once again prime factors=3. If k is 0 there are no prime factors. INSUFFICIENT
Combining S1 and S2: k must be a multiple of both 15 and 10. If k=0, there are no prime factors. If k is any other multiple of both 15 and 10 then prime factors at least include 2,3, and 5 so prime factors are > or = 3. INSUFFICIENT
Therefore the answer should be E

However, OA is C.
Can someone please explain to me where I'm going wrong or am I correct to assume that this is an error.

You are doing everything right till the last assumption about zero.

When we combine statements we have that 2, 3, and 5 are factors of k, so k has at least 3 different prime factors.

As for 0, question can be rephrased as follows: is k divisible by more than 3 different prime factors (is k a multiple of more than 3 prime factors). 0 is divisible by EVERY integer (except zero itself), so 0 is divisible by more than 3 prime factors.

Hope it helps.
_________________
VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 111

Kudos [?]: 422 [0], given: 73

Re: OG 12 Diagnostic DS Error? [#permalink]

Show Tags

22 Sep 2010, 23:18
Thank you so much Bunuel! I totally overlooked that property of 0. Off to update my error log.
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Re: OG 12 Diagnostic DS Error?   [#permalink] 22 Sep 2010, 23:18

Go to page   Previous    1   2   [ 35 posts ]

Similar topics Replies Last post
Similar
Topics:
Does the integer k have at least four different prime factors? 3 09 Mar 2016, 21:12
7 How many distinct factors does positive integer k have? 8 17 Jun 2016, 15:32
3 Does the integer k have at least three different positive 13 19 Feb 2017, 00:33
4 If k is a positive integer, does k have more than 3 differen 5 04 Jun 2015, 02:51
2 Does the integer k have at least three different positive 6 25 Mar 2013, 02:14
Display posts from previous: Sort by