GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jun 2018, 07:37

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k is a positive integer less than 215

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
G
Joined: 03 Mar 2018
Posts: 170
Premium Member CAT Tests
If k is a positive integer less than 215 [#permalink]

Show Tags

New post Updated on: 10 Mar 2018, 07:15
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:17) correct 67% (01:32) wrong based on 49 sessions

HideShow timer Statistics

If k is a positive integer less than 215, and \(\frac{26k}{84}\) is an integer, how many different positive prime factors k can have?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

_________________

Please mention my name in your valuable replies.


Originally posted by itisSheldon on 10 Mar 2018, 03:00.
Last edited by itisSheldon on 10 Mar 2018, 07:15, edited 1 time in total.
Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 667
Location: India
Schools: Rotman '20 (S)
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If k is a positive integer less than 215 [#permalink]

Show Tags

New post Updated on: 10 Mar 2018, 03:48
84 = 2*2*3*7
26=13*2
to be the term integer ,K can be 2*3*7*5

Originally posted by sobby on 10 Mar 2018, 03:23.
Last edited by sobby on 10 Mar 2018, 03:48, edited 1 time in total.
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2816
Location: India
GPA: 3.12
Premium Member
Re: If k is a positive integer less than 215 [#permalink]

Show Tags

New post 10 Mar 2018, 03:41
Hi sobby

K could be 2*3*5*7 = 210(which is less than 215)
The rest of your solution remains the same.
84 can be prime factorized as 2*2*3*7 and 26 as 2*13. 26K/84 can be an integer even if K is 210.

Therefore, K can have a total of 4 prime factors(Option C)
_________________

You've got what it takes, but it will take everything you've got

Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 667
Location: India
Schools: Rotman '20 (S)
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If k is a positive integer less than 215 [#permalink]

Show Tags

New post 10 Mar 2018, 03:47
pushpitkc wrote:
Hi sobby

K could be 2*3*5*7 = 210(which is less than 215)
The rest of your solution remains the same.
84 can be prime factorized as 2*2*3*7 and 26 as 2*13. 26K/84 can be an integer even if K is 210.

Therefore, K can have a total of 4 prime factors(Option C)


ahh , multiplication error ... but still i think , question must say maximum number different of prime factor...
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2816
Location: India
GPA: 3.12
Premium Member
Re: If k is a positive integer less than 215 [#permalink]

Show Tags

New post 10 Mar 2018, 04:02
sobby wrote:
pushpitkc wrote:
Hi sobby

K could be 2*3*5*7 = 210(which is less than 215)
The rest of your solution remains the same.
84 can be prime factorized as 2*2*3*7 and 26 as 2*13. 26K/84 can be an integer even if K is 210.

Therefore, K can have a total of 4 prime factors(Option C)


ahh , multiplication error ... but still i think , question must say maximum number different of prime factor...


Yeah, I agree. Properly wording the question would remove the ambiguity.
_________________

You've got what it takes, but it will take everything you've got

Manager
Manager
User avatar
G
Joined: 16 Sep 2016
Posts: 218
WE: Analyst (Health Care)
Re: If k is a positive integer less than 215 [#permalink]

Show Tags

New post 10 Mar 2018, 04:58
itisSheldon wrote:
If k is a positive integer less than 215, and \(\frac{26k}{84}\) is an integer, how many different positive prime factors does k have?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


IMO B or C. I went ahead with B and got it wrong.

26k /84 is an integer.... hence 42 divides k. 42 = 2*3*7. SO K can has a min of 3 factors... here however we can introduce another prime factor ( unique ofcourse ) of 5 and get 42 * 5 = 210.

So I think the question is very ambiguous either K should be less than a number N such that we cannot include 5 as a prime factor or question should be re-phrased to end with "...how many different prime factors can k have?"

Please give kudos if you liked my explanation.
VP
VP
avatar
G
Joined: 07 Dec 2014
Posts: 1018
If k is a positive integer less than 215 [#permalink]

Show Tags

New post 10 Mar 2018, 12:25
1
itisSheldon wrote:
If k is a positive integer less than 215, and \(\frac{26k}{84}\) is an integer, how many different positive prime factors k can have?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


let x=26k/84
k=84x/26→42x/13
42x/13<215
x<66.5
try 66 no
try 65 yes
(42*65)/13=210=k
prime factors of 210 are 2,3,5,7
4
C
If k is a positive integer less than 215   [#permalink] 10 Mar 2018, 12:25
Display posts from previous: Sort by

If k is a positive integer less than 215

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.