If p is the product of the integers from 1 to 30, inclusive, : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 06:15

### 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 June
Open Detailed Calendar

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

Author Message
Manager
Joined: 04 Jan 2008
Posts: 119
Followers: 3

Kudos [?]: 72 [0], given: 0

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

### Show Tags

05 Sep 2008, 23:24
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:06) wrong based on 1 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Director
Joined: 23 Sep 2007
Posts: 789
Followers: 5

Kudos [?]: 185 [0], given: 0

### Show Tags

05 Sep 2008, 23:36
dancinggeometry 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

C

the product of the integers from 1 to 30, inclusive, contains 3^14 as a factor.
Manager
Joined: 11 Apr 2008
Posts: 202
Followers: 2

Kudos [?]: 17 [0], given: 1

### Show Tags

06 Sep 2008, 16:49
It is the total number of 3 content in 30! which is 14
_________________

Nobody dies a virgin, life screws us all.

Manager
Joined: 04 Jan 2008
Posts: 119
Followers: 3

Kudos [?]: 72 [0], given: 0

### Show Tags

06 Sep 2008, 22:24
OA is C. Bin 2 problem.
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

### Show Tags

08 Sep 2008, 09:28
dancinggeometry 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

30/3 + 30/3^2 (nearest integer < this value )+30/3^3(nearest integer < this value)
= 10+3+1=14
_________________

Smiling wins more friends than frowning

SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 34

Kudos [?]: 867 [0], given: 5

### Show Tags

09 Sep 2008, 02:26
scthakur wrote:
x2suresh wrote:
dancinggeometry 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

30/3 + 30/3^2 (nearest integer < this value )+30/3^3(nearest integer < this value)= 10+3+1=14

What is the logic behind this?

30/3 = 10 (there are 10 numbers which are divisible by 3 .. ( 3,6,9,12,15,18,21,24,27,30)
but, in the above we are missing.. additional threes in 9 =3^2,18=2*3^3,27=3*3^2
to count the second threes that are missing.
30/3^3 =3.33~=3
still we are missing third three in 27 (3^3)
similarly
30/3^3 = 1.11~=1 this will givie the third three from 27

If p is the product of the integers from 1 to 90, inclusive, what is the greatest integer k for which 3^k is a factor of p?

90/3=30
90/9=10
90/27=10/3=3.3~3
90/81=10/9=1.1~1

k=30+10+3+1=45
_________________

Smiling wins more friends than frowning

Re: Zumit PS 001   [#permalink] 09 Sep 2008, 02:26
Display posts from previous: Sort by