NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 22:19 It is currently 23 Apr 2024, 22:19
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

A number is said to be prime saturated if the product of all the diffe

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
amychen77
Intern
Intern
Joined: 17 Oct 2008
Posts: 4
Own Kudos [?]: 108 [108]
Given Kudos: 0
Send PM
A number is said to be prime saturated if the product of all the diffe [#permalink] New post   17 Oct 2008, 10:21
8
Kudos
99
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

72% (02:11) correct 28% (02:00) wrong based on 1242 sessions
Hide Show timer Statistics
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?

A. 99
B. 98
C. 97
D. 96
E. 95
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618638 [52]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   18 Dec 2010, 14:36
24
Kudos
28
Bookmarks
Expert Reply
ajit257 wrote:
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?

a.99
b.98
c.97
d.96
e.95


The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this.

Answer: D.

Or just make prime factorization of all numbers:

A. 99 = 3^2*11 --> 3*11=33>9;
B. 98 = 2*7^2 --> 2*7=14>9;
C. 97 = prime number>9;
D. 96 = 2^5*3 --> 2*3=6<9;
E. 95 = 5*19 --> 5*19=95>9.

Hope it's clear.
User avatar
JohnLewis1980
Senior Manager
Senior Manager
Joined: 21 Apr 2008
Posts: 286
Own Kudos [?]: 102 [10]
Given Kudos: 13
Concentration: Industrial Sector
Schools:Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
 Q47  V28
Send PM
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   19 Oct 2008, 11:44
5
Kudos
5
Bookmarks
Hi guys,

IMO: D

A prime factors are 3 and 11. 33<sqrt(99)? no

B prime factors are 2 and 7. 14<sqrt(98)? no

C prime number. its sqrt is never greater than itself

D A prime factors are 2 and 6. 6<sqrt(96)? yes

E prime factors are 5 and 19. 45<sqrt(95)? no

OA?

Cheers
General Discussion
User avatar
L
carcass
Board of Directors
Joined: 01 Sep 2010
Posts: 4380
Own Kudos [?]: 32863 [2]
Given Kudos: 4453
Send PM
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   19 Dec 2010, 06:51
2
Kudos
your explenation are ALWAYS straightforward...........in each post or reply.

unbelievable :) thanks a lot man
User avatar
B
subhashghosh
Retired Moderator
Joined: 16 Nov 2010
Posts: 909
Own Kudos [?]: 1172 [0]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Send PM
Reviews Badge
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   14 Feb 2011, 19:44
96 = 3 * 32 = 3 * 2^5

Answer is D.
User avatar
L
sashiim20
Director
Director
Joined: 04 Dec 2015
Posts: 620
Own Kudos [?]: 1585 [7]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   11 Dec 2018, 09:35
4
Kudos
3
Bookmarks
amychen77 wrote:
A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?

A. 99
B. 98
C. 97
D. 96
E. 95


Given prime saturated is the product of all the different positive prime factors of \(n\) which is less than the \(\sqrt{n}\).

Checking the answer choices; the highest value is \(99\). \(\sqrt{99}\) is more than \(9\) and less than \(10\).

Lowest value is \(95\). \(\sqrt{95}\) is more than \(9\) and less than \(10\).

Hence the square root of all answer choices are between \(9\) and \(10\).

A. \(99 = 3*3*11\) \(=> 3*11 = 33\)

B. \(98 = 2*7*7\) \(=> 2*7 = 14\)

C. \(97 => 1* 97\)

D. \(96 = 2^5*3\) \(=> 2*3 = 6\). \(=>\) Less than \(\sqrt{96}\).

E. \(95 =>5*19\)

Answer D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32635
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: A number is said to be prime saturated if the product of all the diffe [#permalink] New post   24 Feb 2024, 21:41
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.
GMAT Club Bot
gmatclubot
Re: A number is said to be prime saturated if the product of all the diffe [#permalink]
24 Feb 2024, 21:41
Moderators:
Bunuel
Math Expert
92883 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