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

 It is currently 19 Feb 2019, 18:15

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# If k is a positive integer less than 215

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Mar 2018
Posts: 215
If k is a positive integer less than 215  [#permalink]

### Show Tags

Updated on: 10 Mar 2018, 06:15
1
00:00

Difficulty:

95% (hard)

Question Stats:

41% (01:58) correct 59% (01:55) wrong based on 56 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

_________________

Originally posted by itisSheldon on 10 Mar 2018, 02:00.
Last edited by itisSheldon on 10 Mar 2018, 06:15, edited 1 time in total.
Director
Joined: 14 Nov 2014
Posts: 628
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If k is a positive integer less than 215  [#permalink]

### Show Tags

Updated on: 10 Mar 2018, 02:48
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, 02:23.
Last edited by sobby on 10 Mar 2018, 02:48, edited 1 time in total.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Re: If k is a positive integer less than 215  [#permalink]

### Show Tags

10 Mar 2018, 02:41
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
Joined: 14 Nov 2014
Posts: 628
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If k is a positive integer less than 215  [#permalink]

### Show Tags

10 Mar 2018, 02:47
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...
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Re: If k is a positive integer less than 215  [#permalink]

### Show Tags

10 Mar 2018, 03:02
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

Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 722
Re: If k is a positive integer less than 215  [#permalink]

### Show Tags

10 Mar 2018, 03:58
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.
_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

VP
Joined: 07 Dec 2014
Posts: 1156
If k is a positive integer less than 215  [#permalink]

### Show Tags

10 Mar 2018, 11:25
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, 11:25
Display posts from previous: Sort by

# If k is a positive integer less than 215

 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®.