It is currently 21 Oct 2017, 11:24

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, wha

Author Message
Manager
Joined: 09 Jun 2010
Posts: 71

Kudos [?]: 26 [0], given: 17

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

Show Tags

11 Jul 2010, 02:36
okay, here is the thing !

I was solving 12 O.G book then this question pop up and I had no shortcut for it ! I mean it took me long to do it !

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

I mean if I keep multiplaying each value in order to hit the right one, it will take a lot of time where in GMAT you must spend 1 minute for each a question, is there any shortcut for this type of question ?

thanks

Kudos [?]: 26 [0], given: 17

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1887 [3], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Can I please know the simple method to solve this problem ? [#permalink]

Show Tags

21 Jul 2010, 13:47
3
KUDOS
sstudy wrote:
Can anybody please tell me how to solve this one ?

Que :

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

Thanks,
sstudy

I think it should be 3^k not 3k else the highest number i.e. 18 in the option should be the answer
Now lets take 3^k

power 3 in 30! is 30/3 + 30/3^2 ..... till 3^k < 30

=> power of 3 in 30! = 30/3 + 30/3^2 + 30/27 = 10 + 3 + 1 = 14 ( ignore decimals think logically why)

The general formula is

$$\frac{n}{k}+ \frac{n}{k^2} +\frac{n}{k^3}$$ till $$n>k^m$$
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1887 [3], given: 235

Intern
Joined: 09 Jul 2010
Posts: 10

Kudos [?]: 1 [0], given: 6

Re: Can I please know the simple method to solve this problem ? [#permalink]

Show Tags

21 Jul 2010, 13:49

Kudos [?]: 1 [0], given: 6

Intern
Joined: 04 Aug 2010
Posts: 14

Kudos [?]: 63 [0], given: 0

Show Tags

04 Aug 2010, 04:10
Can anyone demonstrate the following?

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

Kudos [?]: 63 [0], given: 0

Intern
Joined: 04 Aug 2010
Posts: 14

Kudos [?]: 63 [0], given: 0

Show Tags

07 Aug 2010, 21:18
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

Kudos [?]: 63 [0], given: 0

Manager
Joined: 02 Apr 2010
Posts: 93

Kudos [?]: 18 [0], given: 1

Show Tags

07 Aug 2010, 21:47
p = 1x2x3x4x5x6x7x8x9x10x ....x30

There is a 3 after every 2 numbers. Hence total nos of 3s = 10

Hence K = 10?

Think should be A?

Kudos [?]: 18 [0], given: 1

Manager
Joined: 02 Apr 2010
Posts: 93

Kudos [?]: 18 [0], given: 1

Show Tags

08 Aug 2010, 02:45
thks. think i forgot to count the double threes and the triple threes.

Kudos [?]: 18 [0], given: 1

Manager
Joined: 06 Feb 2010
Posts: 170

Kudos [?]: 1408 [0], given: 182

Schools: University of Dhaka - Class of 2010
GPA: 3.63

Show Tags

12 Oct 2010, 04:27
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)20
_________________

Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly

Critical Reasoning: http://gmatclub.com/forum/best-critical-reasoning-shortcuts-notes-tips-91280.html

Collections of MGMAT CAT: http://gmatclub.com/forum/collections-of-mgmat-cat-math-152750.html

MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-of-fourth-edition-152753.html

Sentence Correction: http://gmatclub.com/forum/sentence-correction-strategies-and-notes-91218.html

Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html

I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Kudos [?]: 1408 [0], given: 182

Manager
Status: Will Retake GMAT
Joined: 30 Jul 2010
Posts: 129

Kudos [?]: 15 [0], given: 28

Location: India
Concentration: General Management, Entrepreneurship
Schools: Stanford '13 (D)
GPA: 3.11
WE: Information Technology (Computer Software)

Show Tags

12 Oct 2010, 04:30
This question should be under Quant. Moderators please move it.
_________________

Re-taking GMAT. Hope the charm works this time..

Kudos [?]: 15 [0], given: 28

Manager
Joined: 22 Jun 2010
Posts: 192

Kudos [?]: 127 [0], given: 13

Show Tags

12 Oct 2010, 07:07
:-O come on, it's CR forum buddy

Kudos [?]: 127 [0], given: 13

Manager
Joined: 22 Jun 2010
Posts: 192

Kudos [?]: 127 [0], given: 13

Show Tags

12 Oct 2010, 07:15
anyway let's solve it:
p: 3*6*9*12*15*18*21*24*27*30

P: (3^1)(3*2)(3^2)(3*5)(3^2*2)(3*7)(3*8)(3^3)(3*10)
14

Kudos [?]: 127 [0], given: 13

Manager
Joined: 06 Feb 2010
Posts: 170

Kudos [?]: 1408 [0], given: 182

Schools: University of Dhaka - Class of 2010
GPA: 3.63

Show Tags

12 Oct 2010, 23:57
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)20

I need some great solution to solve this problem quickly.
_________________

Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly

Critical Reasoning: http://gmatclub.com/forum/best-critical-reasoning-shortcuts-notes-tips-91280.html

Collections of MGMAT CAT: http://gmatclub.com/forum/collections-of-mgmat-cat-math-152750.html

MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-of-fourth-edition-152753.html

Sentence Correction: http://gmatclub.com/forum/sentence-correction-strategies-and-notes-91218.html

Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html

I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Kudos [?]: 1408 [0], given: 182

Retired Moderator
Joined: 02 Sep 2010
Posts: 793

Kudos [?]: 1186 [0], given: 25

Location: London
Re: Product of the Integers [#permalink]

Show Tags

13 Oct 2010, 00:17
monirjewel 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)20

I need some great solution to solve this problem quickly.

(30/3)+(30/9)+(30/27)=10+3+1=14

The logic
You need to count the factors of 3 in the product.
So just count all the numbers divisible by 3, which will be (30/3) {3,6,9,...,30}
Now all the numbers divisible by 3^2 or 9 will have 2 factors of 3 so need to count them once more, this will be (30/9) {9,18,27}
And then finally the numbers divisible by 3^3, need to be counted once more, which is (30/27) {27}

No higher powers of 3 will divide numbers <=30, so we are done
_________________

Kudos [?]: 1186 [0], given: 25

Re: Product of the Integers   [#permalink] 13 Oct 2010, 00:17
Display posts from previous: Sort by