It is currently 23 Oct 2017, 10:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the greatest value of q such that 9^q is a factor of 21! ?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129477 [0], given: 12201

What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

13 Dec 2016, 10:52
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:08) correct 41% (01:21) wrong based on 152 sessions

### HideShow timer Statistics

What is the greatest value of q such that 9^q is a factor of 21! ?

A. 1
B. 3
C. 4
D. 5
E. 6
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129477 [0], given: 12201

Senior Manager
Joined: 13 Oct 2016
Posts: 367

Kudos [?]: 396 [0], given: 40

GPA: 3.98
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

13 Dec 2016, 13:15
3
This post was
BOOKMARKED
$$9 = 3^2$$

First we need to find max power of $$3$$ in $$21!$$

$$[\frac{21}{3}] + [\frac{21}{3^2}] = 7 + 2 = 9$$

But we are asked about max power of 9 not 3, so we need to divide our power of 3 by 2 and take integer value.

$$[\frac{9}{2}] = 4$$

$$q=4$$

Answer C.

Kudos [?]: 396 [0], given: 40

Manager
Joined: 13 Dec 2013
Posts: 172

Kudos [?]: 26 [1], given: 122

Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

13 Dec 2016, 14:08
1
This post received
KUDOS
First find the number of 3s in 21! when prime factoring each term. E.g. how many powers of 3 in 21!.

21 -3*7
20 - NA
19 - NA
18 - 2*(3^2)
17 - NA
16 - NA
15 - 5*3
14 - NA
13 - NA
12 - (2^2)*3
11 - NA
10 - NA
9 - 3^2
8 - NA
7 - NA
6 - 2*3
5- NA
4 - NA
3 - 3^1
2 - NA
1 - NA

Totalling up the number of 3s gives 3^9 = (3^2)^4.5 = 9^4.5. Therefore the highest power of 9 must be 4 (5 is larger than 4.5).

Kudos [?]: 26 [1], given: 122

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1088 [1], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

14 Dec 2016, 11:08
1
This post received
KUDOS
Bunuel wrote:
What is the greatest value of q such that 9^q is a factor of 21! ?

A. 1
B. 3
C. 4
D. 5
E. 6

$$9 = 3^2$$

HIghest power of 3 in 21! is 9

21/3 = 7
7/3 = 2

So, the highest power of 9 will be 1/2*9 => 4

Hence, correct answer will be (C) 4

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1088 [1], given: 325

Senior Manager
Joined: 06 Jun 2016
Posts: 263

Kudos [?]: 49 [1], given: 212

Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

16 Dec 2016, 10:34
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
What is the greatest value of q such that 9^q is a factor of 21! ?

A. 1
B. 3
C. 4
D. 5
E. 6

9=3^2
largest power of 3 in 21! is 21/3 + 21/9 = 7+2=9
9^q= 3^9
q=9/2 = 4
C

Kudos [?]: 49 [1], given: 212

Intern
Joined: 03 Apr 2016
Posts: 16

Kudos [?]: 3 [2], given: 6

Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

16 Dec 2016, 11:38
2
This post received
KUDOS
This link is your best friend
http://www.campusgate.co.in/2011/10/fin ... e.html?m=1

Sent from my SAMSUNG-SM-G935A using GMAT Club Forum mobile app

Kudos [?]: 3 [2], given: 6

Manager
Joined: 05 Dec 2016
Posts: 172

Kudos [?]: 18 [1], given: 46

Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

16 Dec 2016, 13:24
1
This post received
KUDOS
9^q=3^2q
To find the answer we it is needed to find the number of powers of 3 in 21!, that equals to 21/3^1 = 7; 21/3^2=2
7+2=9 number of powers of 2 in 21!
Since initial condition is that 3^2q, 9=2q; q=9/2=4,5, therefore maximum power of 3 in 21! is 4. Answer C is correct.

Kudos [?]: 18 [1], given: 46

Intern
Joined: 06 Jan 2016
Posts: 17

Kudos [?]: 8 [1], given: 60

Location: Brazil
Re: What is the greatest value of q such that 9^q is a factor of 21! ? [#permalink]

### Show Tags

15 Sep 2017, 11:18
1
This post received
KUDOS
alados14 wrote:
This link is your best friend
http://www.campusgate.co.in/2011/10/fin ... e.html?m=1

Sent from my SAMSUNG-SM-G935A using GMAT Club Forum mobile app

Thanks for the link, it has helped me to solve my conceptual gap.

Kudos [?]: 8 [1], given: 60

Re: What is the greatest value of q such that 9^q is a factor of 21! ?   [#permalink] 15 Sep 2017, 11:18
Display posts from previous: Sort by

# What is the greatest value of q such that 9^q is a factor of 21! ?

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

 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®.