Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 16:29

### 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 n is the product of the integers from1 to 20 inclusive,

Author Message
Intern
Joined: 17 Sep 2006
Posts: 45
Location: China
Followers: 0

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

If n is the product of the integers from1 to 20 inclusive, [#permalink]

### Show Tags

29 Dec 2006, 17:04
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:39) correct 0% (00:00) wrong based on 16 sessions

### HideShow timer Statistics

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

If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2k is a factor of n?

A 10
B 12
C 15
D 18
E 20
Manager
Joined: 04 Nov 2006
Posts: 158
Followers: 4

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

### Show Tags

29 Dec 2006, 17:53
I must be reading this problem wrong or misunderstanding it. There are many integers k larger than 20 for which 2k is a factor of n=20!.

Of the choices given, each of them, multiplied by 2, is a factor of 20!. So, 20 would be the answer since it asks for the greatest value.

However, take k = 50 as an example. 2k = 100. Is 100 a factor of 20!. Yes, since 20! includes 5*2*10. 50 is larger than 20, so 20 can't be the largest integer for which 2k is a factor of 20!.
Intern
Joined: 17 Sep 2006
Posts: 45
Location: China
Followers: 0

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

### Show Tags

29 Dec 2006, 17:54
sorry~ it was a typo mistake
it should be 2^k
Senior Manager
Joined: 23 Jun 2006
Posts: 387
Followers: 1

Kudos [?]: 322 [0], given: 0

### Show Tags

29 Dec 2006, 18:02
with this correction - 18 is the answer...
there are 10 multiples of 2 in 20!, 5 multiples of 4, 2 multiples of 8 and 1 multiple of 16.

total = 10+5+2+1=18
Senior Manager
Joined: 08 Jun 2006
Posts: 337
Location: Washington DC
Followers: 1

Kudos [?]: 54 [0], given: 0

### Show Tags

30 Dec 2006, 18:39
Getting 18

Just took all the 2s from 1 * 2 * ...20.
Manager
Joined: 23 Dec 2006
Posts: 134
Followers: 1

Kudos [?]: 27 [0], given: 0

### Show Tags

30 Dec 2006, 20:23
I calculate 19 2's between 1-20 inclusive.
Senior Manager
Joined: 05 Oct 2006
Posts: 266
Followers: 1

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

### Show Tags

30 Dec 2006, 21:23
in factorial 20,this way i counted

2 4 6 8 10 12 14 16 18 20 = 10 factors
2 4 6 8 10 =5 factors
2 4 =2 factors
2 = 1 factor

total = 18 factors
Senior Manager
Joined: 24 Nov 2006
Posts: 349
Followers: 1

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

### Show Tags

31 Dec 2006, 00:07
Iawfy wrote:
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A 10
B 12
C 15
D 18
E 20

20! = (product of the odd #s from 1 to 19) * (product of the even #s from 2 to 20) = a * 2*2^2*(2*3)*(2^3)*(2*5)*(2^2*3)*(2*7)*(2^4)*(2*9)*(2^2*5) = aÂ´ * 2^18 => k = 18

(a and a` are abbreviations for the products of the odd numbers that make up 20!).
Manager
Joined: 23 Dec 2006
Posts: 134
Followers: 1

Kudos [?]: 27 [0], given: 0

### Show Tags

31 Dec 2006, 00:12
Oh shoot, I was counting 19 individual 2s, forgetting that one of them is included in 2^18.

I get D, too.
31 Dec 2006, 00:12
Display posts from previous: Sort by

# If n is the product of the integers from1 to 20 inclusive,

 Powered by phpBB © phpBB Group and phpBB SEO 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®.