Last visit was: 14 Jul 2024, 23:06 It is currently 14 Jul 2024, 23:06
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Does the integer k have at least three different positive prime factor

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640869 [25]
Given Kudos: 85011
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640869 [7]
Given Kudos: 85011
General Discussion
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1527 [1]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Manager
Joined: 22 Nov 2010
Posts: 202
Own Kudos [?]: 498 [0]
Given Kudos: 75
Location: India
GMAT 1: 670 Q49 V33
WE:Consulting (Telecommunications)
Re: Does the integer k have at least three different positive prime factor [#permalink]
If a divides b, then all the primes in a along with their powers are in b
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640869 [2]
Given Kudos: 85011
Re: Does the integer k have at least three different positive prime factor [#permalink]
2
Kudos
jdiamond wrote:
Bunuel wrote:
jdiamond wrote:
This is in the official GMAT review book.

Does the integer k have at least three different positive prime factors?

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

The book says
, but shouldn't
the answer be E? Couldn't k = 0?

Merging similar topics. Please refer to the solutions above.

I didn't know this was here already. I don't think my issue with the question is answered in the solutions above.

0 is a multiple of all positive integers. Thus if k=0 it still has at least three different positive prime factors.
Alum
Joined: 12 Aug 2015
Posts: 2271
Own Kudos [?]: 3195 [0]
Given Kudos: 893
GRE 1: Q169 V154
Re: Does the integer k have at least three different positive prime factor [#permalink]

Here is my solution->
We need to check if the number of prime factors of p are atleast 3 i.e.≥3
Statement 1
p=15 => no
p=15*17 => yes
Not sufficient
Statement 2
p=10 => no
p=10*13 => yes
Not sufficient
Combining the two statements we can say that p=2*3*5*x for some integer x.
Clearly p must have atleast 3 prime factors
Hence C
Manager
Joined: 25 Mar 2013
Posts: 166
Own Kudos [?]: 133 [0]
Given Kudos: 101
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: Does the integer k have at least three different positive prime factor [#permalink]
I solved this problem using Plug In

1, If k=30, have 2,3,5 prime factors
If K=75, have 3,5 only
Insufficient
2, If k = 70 , have 2,5,7 prime factors
If k = 80, Only 2,5 prime factors
Insufficient
3, K/15 and K/10
If k=30 2,3,5
K=90 2,3,5 prime factors

Irrespective K value , these only both meet conditions
C

Is my approach Right?
Thanks
Intern
Joined: 05 Sep 2016
Posts: 2
Own Kudos [?]: 2 [1]
Given Kudos: 68
Location: India
Re: Does the integer k have at least three different positive prime factor [#permalink]
1
Bookmarks
Here is my solution:

Question: Does K have at-least 3 different positive prime factors.

Statement 1: $$\frac{k}{15}$$ is an integer.

Hence the values of k are multiples of 15 such as 15,30,45...
Factors of 15 = 5 and 3 (2 factors)
Factors of 30 = 5 , 3 and 2 (3 factors)
Hence not sufficient.

Statement 2: $$\frac{k}{10}$$ is an integer

Hence the values of k are multiples of 10 such as 10,20,30
Factors of 10 = 5 and 2 (2 factors)
Factors of 30 = 5 , 3 and 2 (3 factors)
Hence not sufficient.

Stmt 1 + Stmt 2:

k should be multiples of 10 and 15 such as 30,60...
All these values have atleast 3 positive different prime factors.

Hence C.
Intern
Joined: 16 Jun 2016
Posts: 15
Own Kudos [?]: 13 [2]
Given Kudos: 129
Location: Indonesia
Concentration: Strategy, Technology
GMAT 1: 540 Q42 V20
GPA: 2.9
Re: Does the integer k have at least three different positive prime factor [#permalink]
2
Kudos
Hi, does 1 counted as a prime factor?
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640869 [2]
Given Kudos: 85011
Re: Does the integer k have at least three different positive prime factor [#permalink]
2
Kudos
brightandamen wrote:
Hi, does 1 counted as a prime factor?

No, 1 is not a prime number. The smallest prime is 2.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19130
Own Kudos [?]: 22631 [2]
Given Kudos: 286
Location: United States (CA)
Re: Does the integer k have at least three different positive prime factor [#permalink]
1
Kudos
1
Bookmarks
dzodzo85 wrote:
Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

We need to determine whether k has at least three different prime factors.

Statement One Alone:

k/15 is an integer.

Statement one alone is not sufficient to answer the question. If k = 15, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statement Two Alone:

k/10 is an integer.

Statement two alone is not sufficient to answer the question. If k = 10, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statements One and Two Together:

Using statements one and two, we see that k is a multiple of both 10 and 15, and thus it is a multiple of their least common multiple, which is 30. Since all multiples of 30 have at least three different prime factors, the two statements together are sufficient.

Tutor
Joined: 16 Oct 2010
Posts: 15108
Own Kudos [?]: 66634 [1]
Given Kudos: 436
Location: Pune, India
Re: Does the integer k have at least three different positive prime factor [#permalink]
1
Kudos
Intern
Joined: 28 Jul 2016
Posts: 12
Own Kudos [?]: 14 [0]
Given Kudos: 8
Location: United States (FL)
Concentration: Accounting, Accounting
GMAT 1: 640 Q45 V32
GPA: 3.42
WE:Information Technology (Energy and Utilities)
Re: Does the integer k have at least three different positive prime factor [#permalink]
Could integer k be 0?

If so, both conditions (k/10 is an integer) and (k/15 is an integer) would both be met as 0/anything = 0. Does 0 have an infinite number of prime factors?

Thank you all!
Manager
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 284 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Re: Does the integer k have at least three different positive prime factor [#permalink]
TriumphKai wrote:
Could integer k be 0?

If so, both conditions (k/10 is an integer) and (k/15 is an integer) would both be met as 0/anything = 0. Does 0 have an infinite number of prime factors?

Thank you all!

Hello,

0 is a multiple of all integers except 0 itself. Thus if k=0 it still has at least three different positive prime factors.

Hope it helps !!
Intern
Joined: 26 Dec 2021
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 4
Location: Malaysia
Re: Does the integer k have at least three different positive prime factor [#permalink]
Why can't be k or the 3 factors be negative integers given question didn't state it was positive or greater than 0?
Intern
Joined: 01 Jan 2015
Posts: 14
Own Kudos [?]: 1 [0]
Given Kudos: 956
Does the integer k have at least three different positive prime factor [#permalink]
Hi,

When k is an integer, then K can also be 0 or any other integer.

St1: When K= 0 answer is no
When k= 30 answer is yes

St2: When K= 0 answer is no
When k= 30 answer is yes

St1&2

When K = 0 is again no
When K =30 is again yes

So the answer to this question must be E.
Unless you assume k is a positive integer, then the answer is C. You can’t assume on DS questions.
Intern
Joined: 13 Jun 2020
Posts: 23
Own Kudos [?]: 0 [0]
Given Kudos: 95
Location: India
Re: Does the integer k have at least three different positive prime factor [#permalink]
Quote:
Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

Condition 1 :

K/15 = Integer (I) ; K =15*I = 5*3*I
here 'I' could be anything and not necessary that it will give 3 different prime number

Condition 2 :

K/10 = Integer (I) ; K =10*I = 5*2*I
here 'I' could be anything and not necessary that it will give 3 different prime number,

But if we combine both condition then its LCM is 30 and it will give 3 different prime number

Hope it helps !
Non-Human User
Joined: 09 Sep 2013
Posts: 33971
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: Does the integer k have at least three different positive prime factor [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Does the integer k have at least three different positive prime factor [#permalink]
Moderator:
Math Expert
94342 posts