GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Jul 2020, 06:37

### 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

# n is a positive integer, and k is the product of all integers from 1

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

### Hide Tags

Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 237
n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

04 Nov 2010, 17:15
12
84
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:16) correct 34% (02:20) wrong based on 1055 sessions

### HideShow timer Statistics

n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is

A. 8
B. 12
C. 16
D. 18
E. 24

_________________
I'm the Dumbest of All !!
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 65384
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

04 Nov 2010, 17:28
13
26
shrive555 wrote:
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is

8
12
16
18
24

please share your method. Thanks

$$k$$ is the product of all integers from 1 to $$n$$ inclusive --> $$k=n!$$;

$$k$$ is a multiple of 1440 --> $$n!=1440*p=2^5*3^2*5*p$$, for some integer $$p$$ --> $$n!$$ must have at least 2 in power 5, 3 in power 2 and 5 as its factors. Now, $$7!=2*3*(2^2)*5*(2*3)*7=2^4*3^2*5*7$$ not enough power of 2 --> next #: $$8!=2*3*(2^2)*5*(2*3)*7*(2^3)=2^7*3^2*5*7=1440*(2^2*7)$$ --> so lowest value of $$n$$ is 8.

Answer: A (8).
_________________
##### Most Helpful Community Reply
VP
Joined: 02 Jul 2012
Posts: 1091
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

20 Oct 2012, 23:29
4
8
kapsycumm wrote:
n is a positive integer, and k is the product of all integers from 1 to n inclusive.
If k is a multiple of 1440, then the smallest possible value of n is

A. 8
B. 12
C. 16
D. 18
E. 24

Factorizing 1440, we get $$2^5 * 3^2 * 5^1$$

So, k should have at least five 2s, two 3s and one 5.

a) 8! = 2*3*4*5*6*7*8. Above condition is satisfied. Hence answer is A
##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10697
Location: Pune, India
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

04 Nov 2010, 17:35
10
7
shrive555 wrote:
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is

8
12
16
18
24

please share your method. Thanks

When we say k is the product of all integers from 1 to n, we mean k = n!
Now 1440 = 1.2.3.4.5.6.2
Now if k is a multiple of 1440, it has to be at least 8!. This is so because it cannot be 6! due to the extra 2 factor at the end; it cannot be 7! either, again because the extra 2 in the end will be unaccounted for.
If k = 8! = 1.2.3.4.5.6.7.8, then k = 1440*7*4 i.e. k will be a multiple of 1440.
Answer A
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Status: Planning to retake.
Affiliations: Alpha Psi Omega
Joined: 25 Oct 2010
Posts: 81
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q42 V37
GRE 1: Q630 V680
GPA: 3.16
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

06 Nov 2010, 09:53
Took me 0:37 to do 1440x2 and divide that by the smallest choice to see if it fit. 2880/8=360, so A.

(I know my methods are unorthodox, but what can you do.)
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2326
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

07 Nov 2010, 07:37
rockzom wrote:
Took me 0:37 to do 1440x2 and divide that by the smallest choice to see if it fit. 2880/8=360, so A.

(I know my methods are unorthodox, but what can you do.)

'Unorthodox' is one way of putting it.

I'm not sure I understand why you've done what you did, but we're not looking here for the smallest answer choice which divides some multiple of 1440; it's coincidence that you get the right answer if you try that. If '4' or '5' had instead been the first answer choice, you'd find that 2880/4 or 2880/5 is an integer, but those aren't correct answers to the question. There's a reason Bunuel and Karishma carried out the steps they did.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Senior Manager
Joined: 15 Jun 2010
Posts: 266
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

20 Oct 2012, 22:08
2
kapsycumm wrote:
n is a positive integer, and k is the product of all integers from 1 to n inclusive.
If k is a multiple of 1440, then the smallest possible value of n is

A. 8
B. 12
C. 16
D. 18
E. 24

K= multiple of 1440 ie product of some integer P X 1440. &
K= n! = 1.2.3.4......n

Now lets factorize 1440 = 12 * 12 * 10
Now my objective is to find this multiple 12*12*10 with min possible numbers in n!. Lets go on now......
n= 1*2*(3*4)*5*6*7*8(4 X 2)
Hence 8! is sufficient to get a multiple of 12*12*10

Hence Answer A.
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

15 May 2017, 16:30
tejal777 wrote:
n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is

A. 8
B. 12
C. 16
D. 18
E. 24

Let’s break 1440 into prime factors:

1440 = 144 x 10 = 12 x 12 x 10 = 2^5 x 3^2 x 5^1

Thus, k/(2^5 x 3^2 x 5^1) = integer.

We also know that k is the product of all integers from 1 to n inclusive, or in other words, k = n!.

Let’s check our answer choices:

A. If n = 8, then k = 8! and 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 = 2^3 x 7 x 3 x 2 x 5 x 2^2 x 3 x 2 = 7 x 5 x 3^2 x 2^7 does contain five 2s, two 3s and one 5.

Answer: A
_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Non-Human User
Joined: 09 Sep 2013
Posts: 15443
Re: n is a positive integer, and k is the product of all integers from 1  [#permalink]

### Show Tags

22 Apr 2020, 11:17
1
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.
_________________
Re: n is a positive integer, and k is the product of all integers from 1   [#permalink] 22 Apr 2020, 11:17

# n is a positive integer, and k is the product of all integers from 1

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne