NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 14:45 It is currently 25 Apr 2024, 14:45
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If p is a positive integer and p^2 has total 17 positive factors, then

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Posts: 718
Own Kudos [?]: 2147 [32]
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
Send PM
If p is a positive integer and p^2 has total 17 positive factors, then [#permalink] New post   09 Jun 2019, 09:57
2
Kudos
30
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

57% (02:09) correct 43% (02:22) wrong based on 225 sessions
Hide Show timer Statistics
If p is a positive integer and p^2 has total 17 positive factors, then find the number of positive integers that completely divides p^3 but does not completely divide p?

A. 16
B. 17
C. 21
D. 23
E. 24
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31932 [7]
Given Kudos: 290
Send PM
Reviews Badge
Re: If p is a positive integer and p^2 has total 17 positive factors, then [#permalink] New post   10 Jun 2019, 04:48
4
Kudos
3
Bookmarks
Expert Reply
kiran120680 wrote:
If p is a positive integer and p^2 has total 17 positive factors, then find the number of positive integers that completely divides p^3 but does not completely divide p?

A. 16
B. 17
C. 21
D. 23
E. 24


Number of factors =17


It means we are looking at some square and it is given as \(p^2\).
17 can be broken as multiple of different numbers as only 1*17..

Conversion of number of factors to the exponent


17=1*17=(16+1)
So, \(p^2=a^{16}.....p=a^8\), where a is a prime number.

Value of \(p^3=(a^8)^3=a^{24}\)..
All values between \(a^9\) and \(a^{24}\), both inclusive will divide \(a^{24}\) but not \(a^8\)..
so \(a^9, a^{10},a^{11}...a^{23},a^{24}\)
Number of values = 24-9+1=16

A
General Discussion
User avatar
P
Kritisood
Director
Director
Joined: 21 Feb 2017
Posts: 521
Own Kudos [?]: 1038 [4]
Given Kudos: 1091
Location: India
GMAT 1: 700 Q47 V39
Send PM
Reviews Badge
Re: If p is a positive integer and p^2 has total 17 positive factors, then [#permalink] New post   19 Jun 2020, 03:47
1
Kudos
3
Bookmarks
Number of factors of p^2 is 17
17 can only be written as 17*1
hence p^2 must be equal to P^16 as 16+1 = 17 (where P is a prime no.)
then p = P^8 (no of factors = 8+1=9)
and p^3 = 24 (no of factors = 24+1=25)
Therefore, the no of positive integers that divides p^3, but does not divide p = 25 – 9 = 16
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: If p is a positive integer and p^2 has total 17 positive factors, then [#permalink] New post   26 Aug 2023, 00:04
Asked: If p is a positive integer and p^2 has total 17 positive factors, then find the number of positive integers that completely divides p^3 but does not completely divide p?

p^2 = a^16
p = a^8

Positive integers that completely divides (p^3=a^24) but does not completely divide (p=a^8) = {a^9, a^10,.... a^24}
Number of positive integers that completely divides (p^3=a^24) but does not completely divide (p=a^8) = 24-9+1 = 16

IMO A
GMAT Club Bot
gmatclubot
Re: If p is a positive integer and p^2 has total 17 positive factors, then [#permalink]
26 Aug 2023, 00:04
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions