It is currently 19 Nov 2017, 09:31

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 p is the product of the integers from 1 to 30, inclusive

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

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 29 Nov 2009
Posts: 25

Kudos [?]: 68 [3], given: 3

Location: Bangalore - INDIA
Schools: Duke, NUS,Rutgers
WE 1: Health & Life Science
If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 20 Jun 2010, 23:59
3
This post received
KUDOS
26
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (00:59) correct 28% (01:25) wrong based on 1349 sessions

HideShow timer Statistics

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18
[Reveal] Spoiler: OA

Kudos [?]: 68 [3], given: 3

Expert Post
9 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42250

Kudos [?]: 132697 [9], given: 12335

Re: OG12 - PS [#permalink]

Show Tags

New post 21 Jun 2010, 02:23
9
This post received
KUDOS
Expert's post
16
This post was
BOOKMARKED
divakarbio7 wrote:
If p is the product of the integers from 1 to 30,
inclusive, what is the greatest integer k for which 3k is
a factor of p ?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18

Not sure as to how to approach this problem


Given: \(p=30!=3^k*n\). Question: \(k_{max}=?\).

We should find highest power of 3 in 30!. Finding the power of a prime in n!: everything-about-factorials-on-the-gmat-85592.html or math-number-theory-88376.html (factorials chapter).

So:

\(\frac{30}{3}+\frac{30}{9}+\frac{30}{27}=10+3+1=14\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132697 [9], given: 12335

Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17797 [5], given: 235

Location: Pune, India
Re: official guide 13th ed #116 problem solving [#permalink]

Show Tags

New post 19 Jun 2012, 06:13
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
peter2000 wrote:
p is product of integers from 1 to 30 inclusive, what is the greatest integer k for which3^k is a factor of p?

A)10
B)12
C)14
D)16
E)18

I understand the way the GMAT guide does the problem, I was wondering if there was a quicker way?


Check out this post for an explanation of the method you can use to solve such questions:
http://www.veritasprep.com/blog/2011/06 ... actorials/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17797 [5], given: 235

1 KUDOS received
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 189

Kudos [?]: 258 [1], given: 32

new [#permalink]

Show Tags

New post 23 Jun 2010, 13:38
1
This post received
KUDOS
15. No need to actually find the product of 1 to 30. Just look at the numbers that have factors of 3.

3 = 3
6 = 3 * 2
9 = 3 * 3
12 = 3 * 2 * 2
15 = 3 * 5
18 = 3 * 3 * 2
21 = 3 * 7
24 = 3 * 2 * 2 * 2
27 = 3 * 3 * 3
30 = 3 * 2 * 5

There are 14 3's, so the largest factor of p for 3k is 3*14.

Kudos [?]: 258 [1], given: 32

Senior Manager
Senior Manager
User avatar
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 261

Kudos [?]: 1247 [0], given: 48

GMAT ToolKit User
new [#permalink]

Show Tags

New post 26 Feb 2012, 11:19
\(\frac{30}{3}+\frac{30}{3^2}+\frac{30}{3^3}\)
= 10 + 3 + 1 (ignore the decimals part of each fraction)
= 14
_________________

press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)

Kudos [?]: 1247 [0], given: 48

Senior Manager
Senior Manager
User avatar
B
Joined: 03 Sep 2012
Posts: 364

Kudos [?]: 247 [0], given: 37

Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 01 Oct 2012, 06:50
P = 30!
8
P = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1


Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3

3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3

So we have a total of 14 three's ...

Therefore the maximum value of K can be 14 (C)
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Kudos [?]: 247 [0], given: 37

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1842

Kudos [?]: 2600 [0], given: 362

Location: Canada
Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 16 Aug 2016, 15:56
Expert's post
Top Contributor
1
This post was
BOOKMARKED
divakarbio7 wrote:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18


This question is really asking us to determine the number of 3's "hiding" in the prime factorization of p.

p = (1)(2)(3)(4)(5)(6)(7)(8)(9) . . . (27)(28)(29)(30)
= (1)(2)(3)(4)(5)(2)(3)(7)(8)(3)(3)(10)(11)(3)(4)(13)(14)(3)(5)(16)(17)(3)(3)(2)(19)(20)(3)(7)(22)(23)(3)(8)(25)(26). . . (3)(3)(3)(28)(29)(3)(10)
= (3)^14(other non-3 stuff)

Answer:
[Reveal] Spoiler:
C


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2600 [0], given: 362

Manager
Manager
User avatar
B
Joined: 20 Jan 2017
Posts: 63

Kudos [?]: 7 [0], given: 15

Location: United States (NY)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 24 Jan 2017, 19:52
1) We need to calculate the number of prime factors 3 in the product of all the integers from 1 to 30
2) 30/3=10; 30/9=3; 30/27=1; 10+3+1=14

The correct answer is C.

Kudos [?]: 7 [0], given: 15

Manager
Manager
avatar
S
Joined: 03 Jan 2017
Posts: 197

Kudos [?]: 9 [0], given: 4

Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 25 Mar 2017, 10:20
30/3, 30/9, 30/27
10+3+1=14
Answer is C

Kudos [?]: 9 [0], given: 4

Senior Manager
Senior Manager
User avatar
G
Joined: 04 Sep 2015
Posts: 479

Kudos [?]: 80 [0], given: 18

Location: India
WE: Information Technology (Computer Software)
Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

Show Tags

New post 26 Mar 2017, 00:35
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

product of 1 to 30 includes the multiples of 3 and the number of 3 appear ,count them and add

3-1
6-1
9-2
12-1
15-1
18-2
21-1
24-1
27-3
30-1
=14

Kudos [?]: 80 [0], given: 18

Re: If p is the product of the integers from 1 to 30, inclusive   [#permalink] 26 Mar 2017, 00:35
Display posts from previous: Sort by

If p is the product of the integers from 1 to 30, inclusive

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.